IIR数字滤波器的设计外文文献以及翻译
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IIRDigitaFilterDesignAn important step in the development of a digital filter is the determination of a realizable transfer function G(z) approximating the given frequency response specifications. If an IIR filter is desired,it is also necessary to ensure that G(z) is stable. The process of deriving the transfer function G(z) is called digital filter design. After G(z) has been obtained, the next step is to realize it in the form of a suitable filter structure. In chapter 8,we outlined a variety of basic structures for the realization of FIR and IIR transfer functions. In this chapter,we consider the IIR digital filter design problem. The design of FIR digital filters is treated in chapter 10.First we review some of the issues associated with the filter design problem. A widely used approach to IIR filter design based on the conversion of a prototype analog transfer function to a digital transfer function is discussed next. Typical design examples are included to illustrate this approach. We then consider the transformation of one type of IIR filter transfer function into another type, which is achieved by replacing the complex variable z by a function of z. Four commonly used transformations are summarized. Finally we consider the computer-aided design of IIR digital filter. To this end, we restrict our discussion to the use of matlab in determining the transfer functions.9.1 preliminary considerationsThere are two major issues that need to be answered before one can develop the digital transfer function G(z). The first and foremost issue is the development of a reasonable filter frequency response specification from the requirements of the overall system in which the digital filter is to be employed. The second issue is to determine whether an FIR or IIR digital filter is to be designed. In the section ,we examine these two issues first .Next we review the basic analytical approach to the design of IIR digital filters and then consider the determination of the filter order that meets the prescribed specifications. We also discuss appropriate scaling of the transfer function.9.1.1 Digital Filter SpecificationsAs in the case of the analog filter,either the magnitude and/or the phase(delay) response is specified for the design of a digital filter for most applications. In some situations, the unit sample response or step response may be specified. In most practical applications, the problem of interest is the development of a realizable approximation to a given magnitude response specification. As indicated in section 4.6.3, the phase response of the designed filter can be corrected by cascading it with an allpass section. The design of allpass phase equalizers has received a fair amount of attention in the last few years. We restrict our attention in this chapter to the magnitude approximation problem only. We pointed out in section 4.4.1 that there are four basic types of filters,whose magnitude responses are shown in Figure 4.10. Since the impulse response corresponding to each of these is noncausal and of infinite length, these ideal filters are not realizable. One way of developing a realizable approximation to these filter would be to truncate the impulse response as indicated in Eq.(4.72) for a lowpass filter. The magnitude response of the FIR lowpass filter obtained by truncating the impulse response of the ideal lowpass filter does not have a sharp transition from passband to stopband but, rather, exhibits a gradual "roll-off."Thus, as in the case of the analog filter design problem outlined in section 5.4.1, the magnitude response specifications of a digital filter in the passband and in the stopband are given with some acceptable tolerances. In addition, a transition band is specified between the passband and the stopband to permit the magnitude to drop off smoothly. For example, the magnitude )(j e G of a lowpass filter may be given as shown in Figure7.1. As indicated in the figure, in the passband defined by 0p ωω≤≤, we require that the magnitude approximates unity with an error of p δ±,i.e.,p p j p for e G ωωδδω≤+≤≤-,1)(1.In the stopband, defined by πωω≤≤s ,we require that the magnitude approximates zero with an error of i s ,δ.e.,,)(s j e G δω≤ forπωω≤≤s . The frequencies p ω and s ω are , respectively, called the passband edge frequency and the stopband edge frequency. The limits of the tolerances in the passband and stopband, p δ and s δ, are usually called the peak ripple values. Note that the frequency response )(ωj e G of a digital filter is a periodic function of ω,and the magnitude response of a real-coefficient digital filter is an even function ofω. As a result, the digital filter specifications are given only for the range πω≤≤0.Digital filter specifications are often given in terms of the loss function,)(log 20)(10ωωζj e G -=, in dB. Here the peak passband ripplep α and the minimum stopband attenuations α are given in dB,i.e., the loss specifications of a digitalfilter are given bydB p p )1(log 2010δα--=,dB s s )(log 2010δα-=.9.1 Preliminary ConsiderationsAs in the case of an analog lowpass filter, the specifications for a digital lowpass filter may alternatively be given in terms of its magnitude response, as in Figure 7.2. Here the maximum value of the magnitude in the passband is assumed to be unity, and themaximum passband deviation, denoted as 1/21ε+,is given by the minimum value of the magnitude in the passband. The maximum stopband magnitude is denoted by 1/A.For the normalized specification, the maximum value of the gain function or the minimum value of the loss function is therefore 0 dB. The quantity max α given bydB )1(log 20210max εα+=Is called the maximum passband attenuation. Forp δ<<1, as is typically the case, itcan be shown thatp p αδα2)21(log 2010max ≅--≅ The passband and stopband edge frequencies, in most applications, are specified in Hz, along with the sampling rate of the digital filter. Since all filter design techniques are developed in terms of normalized angular frequencies p ω and s ω,the sepcified critical frequencies need to be normalized before a specific filter design algorithm can be applied. Let T F denote the sampling frequency in Hz, and F P and F s denote, respectively,the passband and stopband edge frequencies in Hz. Then the normalized angular edge frequencies in radians are given byT F F F F p TpT p p ππω22==Ω= T F F F F s T s T s s ππω22==Ω= 9.1.2 Selection of the Filter TypeThe second issue of interest is the selection of the digital filter type,i.e.,whether an IIR or an FIR digital filter is to be employed. The objective of digital filter design is to develop a causal transfer function H(z) meeting the frequency response specifications. For IIR digital filter design, the IIR transfer function is a real rational function of 1-z . H(z)=N MdNzz d z d d pMz z p z p p ------++++++++ (2211022110)Moreover, H(z) must be a stable transfer function, and for reduced computational complexity, it must be of lowest order N. On the other hand, for FIR filter design, the FIR transfer function is a polynomial in 1-z:∑=-=Nnnz nhzH] [)(For reduced computational complexity, the degree N of H(z) must be as small as possible.In addition, if a linear phase is desired, then the FIR filter coefficients must satisfy the constraint:][][Nnhnh-±=T here are several advantages in using an FIR filter, since it can be designed with exact linear phase and the filter structure is always stable with quantized filter coefficients. However, in most cases, the order N FIR of an FIR filter is considerably higher than the order N IIR of an equivalent IIR filter meeting the same magnitude specifications. In general, the implementation of the FIR filter requires approximately N FIR multiplications per output sample, whereas the IIR filter requires 2N IIR+1 multiplications per output sample. In the former case, if the FIR filter is designed with a linear phase, then the number of multiplications per output sample reduces to approximately (N FIR+1)/2. Likewise, most IIR filter designs result in transfer functions with zeros on the unit circle,and the cascade realization of an IIR filter of orderIIRN with all of the zeros on the unitcircle requires [(3IIRN+3)/2] multiplications per output sample. It has been shown that for most practical filter specifications, the ratio N FIR/N IIR is typically of the order of tens or more and, as a result, the IIR filter usually is computationally more efficient[Rab75]. However ,if the group delay of the IIR filter is equalized by cascading it with an allpass equalizer, then the savings in computation may no longer be that significant [Rab75]. In many applications, the linearity of the phase response of the digital filter is not an issue,making the IIR filter preferable because of the lower computational requirements.9.1.3 Basic Approaches to Digital Filter DesignIn the case of IIR filter design, the most common practice is to convert the digital filter specifications into analog lowpass prototype filter specifications, and then to transform it into the desired digital filter transfer function G(z). This approach has been widely used for many reasons:(a) Analog approximation techniques are highly advanced.(b) They usually yield closed-form solutions.(c) Extensive tables are available for analog filter design.(d) Many applications require the digital simulation of analog filters.In the sequel, we denote an analog transfer function as)()()(s D s P s H a a a =, Where the subscript "a" specifically indicates the analog domain. The digital transfer function derived form H a (s) is denoted by)()()(z D z P z G = The basic idea behind the conversion of an analog prototype transfer function H a (s) into a digital IIR transfer function G(z) is to apply a mapping from the s-domain to the z-domain so that the essential properties of the analog frequency response are preserved. The implies that the mapping function should be such that(a) The imaginary(j Ω) axis in the s-plane be mapped onto the circle of the z-plane.(b) A stable analog transfer function be transformed into a stable digital transfer function.To this end,the most widely used transformation is the bilinear transformation described in Section 9.2.Unlike IIR digital filter design,the FIR filter design does not have any connection with the design of analog filters. The design of FIR filter design does not have anyconnection with the design of analog filters. The design of FIR filters is therefore based on a direct approximation of the specified magnitude response,with the often added requirement that the phase response be linear. As pointed out in Eq.(7.10), a causal FIR transfer function H(z) of length N+1 is a polynomial in z -1 of degree N. The corresponding frequency response is given by∑=-=N n n j j en h e H 0][)(ωω.It has been shown in Section 3.2.1 that any finite duration sequence x[n] of length N+1 is completely characterized by N+1 samples of its discrete-time Fourier transfer X(ωj e ). As a result, the design of an FIR filter of length N+1 may be accomplished by finding either the impulse response sequence {h[n]} or N+1 samples of its frequency response )H(e j ω. Also, to ensure a linear-phase design, the condition of Eq.(7.11) must be satisfied. Two direct approaches to the design of FIR filters are the windowed Fourier series approach and the frequency sampling approach. We describe the former approach in Section 7.6. The second approach is treated in Problem 7.6. In Section 7.7 we outline computer-based digital filter design methods.作者:Sanjit K.Mitra国籍:USA出处:Digital Signal Processing -A Computer-Based Approach 3eIIR数字滤波器的设计在一个数字滤波器发展的重要步骤是可实现的传递函数G(z)的接近给定的频率响应规格。
学科分类号本科毕业设计题目(中文):基于DSP的IIR滤波器设计(英文):The Design of IIR Filter Basedon DSP Chip姓名学号院(系)专业、年级指导教师二〇年月目录摘要 (1)Abstract. (2)1 绪论 (2)1.1 认识数字信号处理和IIR数字滤波器 (3)1.2 数字滤波器的实现方法 (4)1.3 主要研究内容 (6)2 滤波器原理基础 (6)2.1 IIR数字滤波器的优缺点 (7)2.2 IIR数字滤波器的设计方法和原理 (9)2.2.1 脉冲响应不变法 (12)2.2.2 双线性变换法 (14)2.3 IIR滤波器的基本结构 (17)3 IIR滤波器的设计过程及DSP的实现 (21)3.1 IIR滤波器的设计过程 (21)3.2 DSP系统的设计流程 (22)3.3 IIR数字滤波器在DSP上的实现 (22)参考文献 (27)附录 (28)致谢 (31)外文文献译文......................................................................................... 1-3 外文文献原文基于DSP的IIR滤波器设计摘要:数字信号处理(Digital Signal Processing,DSP)是一门涉及许多学科而又广泛应用于众多领域的新兴学科。
早在20世纪60年代,数字信号处理(即信号的数字化及数字处理)理论已经被被提出,到20世纪70年代,DSP理论和算法基础才被人提出。
不久之后,1982年世界上第一枚DSP芯片诞生了。
这枚DSP芯片在当时运算速度很快,尤其是在编码解码和语音合成方面得到广泛应用。
随着科学技术的飞速发展,数字化硬件技术得到长足的发展,这就带动了数字信号处理的飞速发展,也使得它得到了很多的实际应用,由此奠定了DSP这一词的地位。
之后,DSP芯片的科研不断推陈出新,每一代的DSP芯片都向着使运算速度更快、精度更高的目标发展,应用于通信、语音、医疗、仪器仪表和家用电器等人类生产生活的各个领域。
I. 简介Matlab是一种非常常用的科学计算软件,它广泛用于信号处理、图像处理、控制系统等领域。
在信号处理中,IIR(Infinite Impulse Response)滤波器是一种常见的数字滤波器,常被用于模拟滤波、数字滤波等应用中。
这篇文章将介绍如何使用Matlab进行IIR低通滤波器的设计。
II. 什么是IIR低通滤波器1. IIR滤波器IIR滤波器是一种数字滤波器,其特点是其单位脉冲响应是无限长的。
它通常具有较为复杂的频率响应特性,且具有较小的阶数,能够更好地逼近某些复杂的频率响应曲线。
IIR滤波器分为低通滤波器、高通滤波器、带通滤波器和带阻滤波器等。
2. 低通滤波器低通滤波器是一种常见的滤波器,其特点是只允许低频信号通过,而抑制高频信号。
在信号处理中,低通滤波器常被用于去除高频噪声、提取低频信号等应用中。
III. Matlab中的IIR低通滤波器设计1. 使用Matlab进行IIR低通滤波器设计Matlab提供了丰富的信号处理工具箱,包括了数字滤波器设计工具。
在Matlab中,可以使用函数butter、cheby1、cheby2、ellip等来设计IIR低通滤波器。
2. 设计步骤设计IIR低通滤波器的一般步骤如下:a. 确定通带和阻带的频率范围b. 选择滤波器的通带和阻带的最大允许衰减c. 选择滤波器的类型(Butterworth、Chebyshev等)以及阶数d. 使用Matlab中相应的函数设计滤波器e. 对设计的滤波器进行频率响应分析IV. 实例分析以下是一个在Matlab中设计IIR低通滤波器的简单实例:设计IIR低通滤波器fs = 1000; 采样频率fpass = 100; 通带截止频率fstop = 200; 阻带截止频率apass = 1; 通带最大允许衰减astop = 80; 阻带最小要求衰减[num, den] = butter(4, fpass/(fs/2), 'low');freqz(num, den, 512, fs); 绘制滤波器频率响应曲线V. 结论使用Matlab进行IIR低通滤波器设计是一种简单而有效的方法。
摘要在本文中,我们分别研究了在MATLAB环境下IIR数字滤波器的典型设计和完全设计等方法。
典型设计是先按一定规则将给出的数字滤波器的技术指标转换成模拟低通滤波器的技术指标,据此产生模拟滤波器原型,然后把模拟低通滤波器原型转换成模拟低通、高通、带通、带阻滤波器,最后再把模拟滤波器转换成数字滤波器。
完全设计方法中我们利用函数直接设计出低通、高通、带通和带阻滤波器,并分别用巴特沃斯(Butterworth )滤波器、切比雪夫( Chebyshev )滤波器、椭圆(Cauer )滤波器来实现,并比较了各自的频率响应曲线。
在FIR滤波器的设计中,我们用切比雪夫窗和海明窗设计的带通滤波器的频率响应进行对照,结果表面用海明窗设计的滤波器的频率特性几乎在任何频带上都比切比雪夫窗设计的滤波器的频率特性好,只是海明窗设计的滤波器下降斜度较小。
本文利用不同的滤波器研究了MATLAB环境下的图像处理技术。
对一张无锡马山园林的风景照片进行的二种修正,取得了不同的效果。
先对原图进行线性变换增加了对比度和亮度对这张图像,图像效果有了一定的改善。
后来我们用非锐化滤波器对修正后的图像再进行了处理,对图像的过渡失真进行了补偿。
本文还对一幅加噪声婚纱照片的去噪效果进行了研究。
比较去噪效果证明,用小波变换的方法进行去噪,图像处理效果更佳。
关键词:数字滤波器;图像处理;小波变换作者:王海楠指导教师:王婷婷AbstractIn this thesis, the typical and complete designs under MATLAB are studied.The typical design gets the technical parameters from digital filters that should be designed, and then transformed into the analog parameters of a low-pass analog filter prototype. The prototype is converted into the analog low-pass, high-pass, band-pass and the band-stop filters respectively, which are transformed into the digital ones.The complete design uses the given functions and releases the low-pass,high-pass,band-pass and the band-stop filters directly. Butterworth, Chebyshev and Caoer filters are used for the implementations.In the FIR filter designs, Chebyshev and Hamming windows are used for abmd-pass filter. Their frequency responses are compared. The advantage of Hamming window is shown on all bands.Finally, the image processing functions using filters under MATLAB are photo (Wuxi Garden) is modified with two different processes and the different effects can be seen. The linear transformation improved the contrast and brightness of the photo, while the un-sharpening filter compensated the transitions.Another photo is modified with the wavelet transformation, which shows the better effects on reducing noises.Keywords: digital filter; image processing; wavelet transformationAuthor: Wang HainanDirected by Wang Tingting第1章绪论数字滤波在通信、图像编码、语音编码、雷达等许多领域中有着十分广泛的应用。
一、实验题目:IIR数字滤波器设计(Ⅰ)二、实验内容:数字滤波器是对数字信号实现滤波的线性时不变系统。
数字滤波实质上是一种运算过程,实现对信号的运算处理。
输入数字信号(数字序列)通过特定的运算转变为输出的数字序列,因此,数字滤波器本质上是一个完成特定运算的数字计算过程,也可以理解为是一台计算机。
描述离散系统输出与输入关系的卷积和差分方程只是给数字信号滤波器提供运算规则,使其按照这个规则完成对输入数据的处理。
时域离散系统的频域特性:,其中、分别是数字滤波器的输出序列和输入序列的频域特性(或称为频谱特性),是数字滤波器的单位取样响应的频谱,又称为数字滤波器的频域响应。
输入序列的频谱经过滤波后,因此,只要按照输入信号频谱的特点和处理信号的目的,适当选择,使得滤波后的满足设计的要求,这就是数字滤波器的滤波原理。
数字滤波器根据其冲激响应函数的时域特性,可分为两种,即无限长冲激响应(IIR)数字滤波器和有限长冲激响应(FIR)数字滤波器。
IIR 数字滤波器的特征是,具有无限持续时间冲激响应,需要用递归模型来实现,其差分方程为:系统函数为:设计IIR滤波器的任务就是寻求一个物理上可实现的系统函数H(z),使其频率响应H(z)满足所希望得到的频域指标,即符合给定的通带截止频率、阻带截止频率、通带衰减系数和阻带衰减系数。
设计一个数字巴特沃斯低通滤波器,设计指标如下:W p=0.2Π, R P=1dBW s=0.3Π, A s=15dB采样时间间隔S。
T1三、实验要求:(1)用单位冲激响应不变变换法进行设计。
(2)给出详细的滤波器设计说明书。
(3)给出经过运行是正确的程序清单并加上详细的注释。
(4)画出所设计滤波器的幅度特性和相位特性。
四.程序与实验说明:1.利用模拟滤波器设计IIR数字滤波器方法(1)根据所给出的数字滤波器性能指标计算出相应的模拟滤波器的设计指标。
(2)根据得出的滤波器性能指标设计出相应的模拟滤波器的系统函数H(S)。
IIR低通滤波器设计IIR低通滤波器(Infinite Impulse Response Low-pass Filter)是一种常见的数字信号处理滤波器,用于滤除高频信号,保留低频信号。
IIR滤波器的特点是具有无限长的脉冲响应,并且能够在频域中实现既定的频率响应。
IIR滤波器设计的基本原理是将一个连续时间的系统函数转换为差分方程,并通过对这个差分方程进行优化来设计滤波器。
IIR滤波器通常由二阶或更高阶的差分方程组成,每个阶段包含一个延迟线和一个系数。
通过调整各个系数的值,可以修改滤波器的频率响应。
1.确定滤波器的需求:首先需要确定滤波器的截止频率和通带衰减等参数。
这些参数决定了滤波器的性能和适用范围。
2. 选择滤波器结构:根据应用的需求和性能要求,选择合适的IIR 滤波器结构。
常见的结构包括Butterworth滤波器、Chebyshev滤波器和Elliptic滤波器等。
3.转换为频率响应函数:将低通滤波器的幅度响应转换为特定形式的频率响应函数。
常见的响应函数包括单位增益的低通滤波器响应和指定范围内的最小相位响应等。
4.选择滤波器阶数:通过调整滤波器的阶数,可以改变滤波器的频率响应特性。
增加阶数可以获得更陡峭的滚降特性,但也会增加计算和存储空间的需求。
5.设计滤波器系数:根据所选择的滤波器结构和阶数,使用合适的设计方法计算滤波器的系数。
常见的设计方法包括频率变换法、极点截断法和最优化设计等。
6. 实现滤波器:将滤波器的差分方程转换为数字信号处理器(DSP)或嵌入式系统中的实际滤波器。
可以使用直接形式、级联形式或者Lattice滤波器结构等不同的实现方式。
7.评估滤波器性能:使用测试数据对设计的滤波器进行评估,并根据需要对滤波器进行调整和优化。
可以使用频率相应曲线、群延迟响应和信号波形等多种方法进行性能评估。
总结来说,设计IIR低通滤波器的过程涉及滤波器需求的确定、结构的选择、频率响应函数的转换、阶数和系数的设定、滤波器实现和性能评估等多个方面。
IIR数字滤波器设计摘要数字滤波器是具有一定传输选择特性的数字信号处理装置,其输入、输出均为数字信号,实质上是一个由有限精度算法实现的线性时不变离散系统。
它的基本工作原理是利用离散系统特性对系统输入信号进行加工和变换,改变输入序列的频谱或信号波形,让有用频率的信号分量通过,抑制无用的信号分量输出。
数字滤波器和模拟滤波器有着相同的滤波概念,根据其频率响应特性可分为低通、高通、带通、带阻等类型,与模拟滤波器相比,数字滤波器除了具有数字信号处理的固有优点外,还有滤波精度高(与系统字长有关)、稳定性好(仅运行在0与l 两个电平状态)、灵活性强等优点。
数字滤波器按单位脉冲响应的性质可分为无限长单位脉冲响应滤波器IIR和有限长单位脉冲响应滤波器(FIR)两种。
本文介绍IIR数字滤波器的设计[4]。
关键词:IIR FIRAbstractDigital filter is a digital filter has the certain transmission choicecharacteristic isdigital signal processing device, signal processing device has the certain transmission choicecharacteristic,Is essentially a realization by the finite precision arithmetic and linear time invariant discrete systems。
Its basic principle is to use the characteristics of discrete system for processing and transformation of system input signal,To change the input sequence spectrum or signal waveform,Let the signal components useful frequency by suppression of signal components, the output of useless。
IIR数字滤波器的设计步骤1.简介I I R(In fi ni te Im pu l se Re sp on se)数字滤波器是一种常用的数字信号处理技术,它的设计步骤可以帮助我们实现对信号的滤波和频率选择。
本文将介绍I IR数字滤波器的设计步骤。
2.设计步骤2.1确定滤波器的类型I I R数字滤波器的类型分为低通滤波器、高通滤波器、带通滤波器和带阻滤波器。
根据信号的要求,我们需确定所需滤波器的类型。
2.2确定滤波器的规格根据滤波器的应用场景和信号特性,我们需确定滤波器的通带范围、阻带范围和衰减要求。
2.3选择滤波器的原型常用的I IR数字滤波器有巴特沃斯滤波器、切比雪夫滤波器和椭圆滤波器等。
根据滤波器的需求,我们需选择适合的滤波器原型。
2.4设计滤波器的传递函数根据滤波器的规格和选定的滤波器原型,我们需计算滤波器的传递函数。
传递函数表示了输入和输出之间的关系,可以帮助我们设计滤波器的频率响应。
2.5对传递函数进行分解将滤波器的传递函数进行分解,可得到II R数字滤波器的差分方程。
通过对差分方程进行相关计算,可以得到滤波器的系数。
2.6滤波器的稳定性判断根据滤波器的差分方程,判断滤波器的稳定性。
稳定性意味着滤波器的输出不会无限增长,确保了滤波器的可靠性和准确性。
2.7选择实现方式根据滤波器的设计需求和实际应用场景,我们需选择I IR数字滤波器的实现方式。
常见的实现方式有直接I I型、级联结构和并行结构等。
2.8优化滤波器性能在设计滤波器后,我们可以对滤波器的性能进行优化。
优化包括滤波器的阶数和抗混淆能力等方面。
3.总结I I R数字滤波器的设计步骤包括确定滤波器的类型和规格、选择滤波器的原型、设计滤波器的传递函数、对传递函数进行分解、判断滤波器的稳定性、选择实现方式和优化滤波器性能等。
通过这些步骤的实施,我们可以有效地设计出满足信号处理需求的II R数字滤波器。
iir数字滤波器的设计什么是iir数字滤波器?iir(infinite impulse response)数字滤波器是一种数字滤波器,与fir(finite impulse response)数字滤波器不同。
与fir数字滤波器只要考虑最近的输入和输出有关,因此具有有限的冲击响应,iir数字滤波器具有无限的冲击响应,因为它们可以让输出与过去的输入有关。
在iir数字滤波器中,有反馈路径,这是与fir数字滤波器不同的。
这意味着,iir滤波器依赖于以前的输出和输入来计算当前的输出。
iir数字滤波器的应用iir数字滤波器在数码信号处理中得到了广泛应用,可以用于各种应用,包括:•音频处理:包括音频滤波器,均衡器和调音台等•通信:数字化通信和语音处理•生产控制:包括传感器计算和控制器如何设计iir数字滤波器?要设计iir数字滤波器,我们需要考虑几个步骤。
1. 确定数字滤波器的类型在设计iir数字滤波器之前,我们需要先确定所需的数字滤波器类型。
通常,数字滤波器可以分为以下两类:•低通滤波器(LPF)•高通滤波器(HPF)根据所需的应用程序和系统需求,您可以确定所需的滤波器类型。
2. 确定滤波器规格在设计iir数字滤波器之前,我们需要确定所需的滤波器规格。
这包括通带和阻带频率,通带和阻带增益等。
3. 选择设计工具在选择设计工具时,可以使用以下工具:•Matlab•Python4. 根据设计规格进行设计使用所选的设计工具,我们可以根据滤波器规格进行设计。
例如,我们可以使用Matlab中的dsp工具箱设计数字滤波器。
Fs = 1000; % 采样频率Fpass = 200; % 通带频率Fstop = 300; % 阻带频率Apass = 1; % 通带最大衰减Astop = 80; % 阻带最小衰减% 将数字滤波器设计为低通滤波器,并使用butterworth滤波器设计方法d = fdesign.lowpass('Fp,Fst,Ap,Ast',Fpass,Fstop,Apass,Astop,Fs);Hd = design(d,'butter');% 将数字滤波器设计为高通滤波器,并使用chebyshev滤波器设计方法d = fdesign.highpass('Fst,Fp,Ast,Ap',Fpass,Fstop,Astop,Apass,Fs);Hd = design(d,'cheby1');以上示例演示了如何使用Matlab中的dsp工具箱设计数字低通滤波器和数字高通滤波器。
iir数字滤波器的设计实验报告IIR数字滤波器的设计实验报告引言数字滤波器是数字信号处理中的重要组成部分,用于去除信号中的噪声、滤波、频率分析等。
在数字滤波器中,IIR(Infinite Impulse Response)滤波器是一种常见且广泛应用的滤波器类型。
本实验旨在设计一个IIR数字滤波器,并通过实验验证其性能。
一、实验目的本实验的目标是设计一个IIR数字滤波器,实现对输入信号的滤波功能。
具体而言,我们将通过以下步骤完成实验:1. 确定滤波器的滤波类型(低通、高通、带通或带阻)和截止频率。
2. 设计滤波器的传递函数。
3. 使用Matlab或其他数学软件进行滤波器的频率响应和时域响应分析。
4. 利用实验数据对滤波器进行性能评估。
二、实验原理IIR数字滤波器的设计基于差分方程,其传递函数可以表示为:H(z) = (b0 + b1*z^(-1) + b2*z^(-2) + ... + bn*z^(-n)) / (1 + a1*z^(-1) +a2*z^(-2) + ... + am*z^(-m))其中,b0、b1、...、bn和a1、a2、...、am是滤波器的系数。
滤波器的阶数为max(m, n)。
根据滤波器的滤波类型和截止频率,可以确定这些系数的具体值。
三、实验步骤1. 确定滤波器的类型和截止频率。
例如,我们选择设计一个低通滤波器,截止频率为1kHz。
2. 根据所选滤波器类型和截止频率,计算滤波器的传递函数。
3. 使用Matlab或其他数学软件进行滤波器的频率响应和时域响应分析。
可以绘制滤波器的幅频响应曲线和相频响应曲线,以及滤波后的信号波形。
4. 利用实验数据对滤波器进行性能评估。
可以通过输入不同频率的信号,观察滤波器的效果,并计算滤波器的截止频率、增益和相位特性等参数。
四、实验结果与分析通过实验,我们得到了设计的低通滤波器的频率响应和时域响应曲线。
在频率响应曲线中,我们可以观察到滤波器在截止频率附近的衰减特性,以及在截止频率以下的通过特性。
iir数字滤波器设计及c语言程序IIR数字滤波器设计及C语言程序IIR(Infinite Impulse Response)数字滤波器是一种常用的数字信号处理技术,广泛应用于音频处理、图像处理、通信系统等领域。
本文将介绍IIR数字滤波器的设计原理,并给出相应的C语言程序实现。
一、IIR数字滤波器的设计原理IIR数字滤波器的设计基于差分方程,其输入信号和输出信号之间存在一定的差分关系。
相比于FIR(Finite Impulse Response)数字滤波器,IIR数字滤波器具有更窄的转换带宽、更高的滤波器阶数和更好的相位响应等特点。
IIR数字滤波器的设计主要包括两个关键步骤:滤波器规格确定和滤波器参数计算。
首先,根据实际需求确定滤波器的类型(低通、高通、带通或带阻)、截止频率、通带衰减和阻带衰减等规格。
然后,根据这些规格利用数字滤波器设计方法计算出滤波器的系数,从而实现对输入信号的滤波。
二、IIR数字滤波器的设计方法常见的IIR数字滤波器设计方法有脉冲响应不变法、双线性变换法和最小均方误差法等。
下面以最常用的脉冲响应不变法为例介绍设计方法。
脉冲响应不变法的基本思想是将模拟滤波器的脉冲响应与数字滤波器的单位脉冲响应进行匹配。
首先,根据模拟滤波器的传递函数H(s)确定其脉冲响应h(t)。
然后,将连续时间下的脉冲响应离散化,得到离散时间下的单位脉冲响应h[n]。
接下来,根据单位脉冲响应h[n]计算出数字滤波器的差分方程系数,从而得到滤波器的数字表示。
三、IIR数字滤波器的C语言程序实现下面给出一个简单的IIR数字滤波器的C语言程序实现示例,以低通滤波器为例:```c#include <stdio.h>#define N 100 // 输入信号长度#define M 5 // 滤波器阶数// IIR数字滤波器系数float b[M+1] = {0.1, 0.2, 0.3, 0.2, 0.1};float a[M+1] = {1.0, -0.5, 0.3, -0.2, 0.1};// IIR数字滤波器函数float IIR_filter(float *x, float *y, int n) {int i, j;float sum;for (i = 0; i < n; i++) {sum = 0;for (j = 0; j <= M; j++) { if (i - j >= 0) {sum += b[j] * x[i - j]; }}for (j = 1; j <= M; j++) { if (i - j >= 0) {sum -= a[j] * y[i - j]; }}y[i] = sum;}}int main() {float x[N]; // 输入信号float y[N]; // 输出信号int i;// 生成输入信号for (i = 0; i < N; i++) {x[i] = i;}// IIR数字滤波器滤波IIR_filter(x, y, N);// 输出滤波后的信号for (i = 0; i < N; i++) {printf("%f ", y[i]);}return 0;}```以上是一个简单的IIR数字滤波器的C语言程序实现示例。
2013 届毕业设计(论文)英文文献及其翻译资料院、部:电气与信息工程学院学生姓名:指导教师:职称专业:电子信息工程班级:完成时间:2013年6月7日Signal processingSignal processing is an area of electrical engineering and applied mathematics that deals with operations on or analysis of signals, in either discrete or continuous time, to perform useful operations on those signals. Signals of interest can include sound, images, time-varying measurement values and sensor data, for example biological data such as electrocardiograms, control system signals, telecommunication transmission signals such as radio signals, and many others. Signals are analog or digital electrical representations of time-varying or spatial-varying physical quantities. In the context of signal processing, arbitrary binary data streams and on-off signalling are not considered as signals, but only analog and digital signals that are representations of analog physical quantities.HistoryAccording to Alan V. Oppenheim and Ronald W. Schafer, the principles of signal processing can be found in the classical numerical analysis techniques of the 17th century. They further state that the "digitalization" or digital refinement of these techniques can be found in the digital control systems of the 1940s and 1950s.Categories of signal processingAnalog signal processingAnalog signal processing is for signals that have not been digitized, as in classical radio, telephone, radar, and television systems. This involves linear electronic circuits such as passive filters, active filters, additive mixers, integrators and delay lines. It also involves non-linear circuits such as compandors, multiplicators (frequency mixers and voltage-controlled amplifiers), voltage-controlled filters, voltage-controlled oscillators and phase-locked loops.Discrete time signal processingDiscrete time signal processing is for sampled signals that are considered as defined only at discrete points in time, and as such are quantized in time, but not in magnitude.Analog discrete-time signal processing is a technology based on electronic devices such as sample and hold circuits, analog time-division multiplexers, analog delay lines and analog feedback shift registers. This technology was a predecessor of digital signal processing (see below), and is still used in advanced processing of gigahertz signals.The concept of discrete-time signal processing also refers to a theoretical discipline that establishes a mathematical basis for digital signal processing, without taking quantization error into consideration.Digital signal processingDigital signal processing is for signals that have been digitized. Processing is done by general-purpose computers or by digital circuits such as ASICs, field-programmable gate arrays or specialized digital signal processors (DSP chips). Typical arithmetical operations include fixed-point and floating-point, real-valued and complex-valued, multiplication and addition. Other typical operations supported by the hardware are circular buffers and look-up tables. Examples of algorithms are the Fast Fourier transform (FFT), finite impulse response (FIR) filter, Infinite impulse response (IIR) filter, and adaptive filters such as the Wiener and Kalman filters1.Digital signal processingDigital signal processing (DSP) is concerned with the representation of signals by a sequence of numbers or symbols and the processing of these signals. Digital signal processing and analog signal processing are subfields of signal processing. DSP includes subfields like: audio and speech signal processing, sonar and radar signal processing, sensor array processing, spectral estimation, statistical signal processing, digital image processing, signal processing for communications, control of systems, biomedical signal processing, seismic data processing, etc.The goal of DSP is usually to measure, filter and/or compress continuous real-world analog signals. The first step is usually to convert the signal from an analog to a digital form, by sampling it using an analog-to-digital converter (ADC), which turns the analog signal into a stream of numbers. However, often, the required output signal is another analog output signal, which requires a digital-to-analogconverter (DAC). Even if this process is more complex than analog processing and has a discrete value range, the application of computational power to digital signal processing allows for many advantages over analog processing in many applications, such as error detection and correction in transmission as well as data compression.[1]DSP algorithms have long been run on standard computers, on specialized processors called digital signal processors (DSPs), or on purpose-built hardware such as application-specific integrated circuit (ASICs). Today there are additional technologies used for digital signal processing including more powerful general purpose microprocessors, field-programmable gate arrays (FPGAs), digital signal controllers (mostly for industrial apps such as motor control), and stream processors, among others.[2]2. DSP domainsIn DSP, engineers usually study digital signals in one of the following domains: time domain (one-dimensional signals), spatial domain (multidimensional signals), frequency domain, autocorrelation domain, and wavelet domains. They choose the domain in which to process a signal by making an informed guess (or by trying different possibilities) as to which domain best represents the essential characteristics of the signal. A sequence of samples from a measuring device produces a time or spatial domain representation, whereas a discrete Fourier transform produces the frequency domain information, that is the frequency spectrum. Autocorrelation is defined as the cross-correlation of the signal with itself over varying intervals of time or space.3. Signal samplingMain article: Sampling (signal processing)With the increasing use of computers the usage of and need for digital signal processing has increased. In order to use an analog signal on a computer it must be digitized with an analog-to-digital converter. Sampling is usually carried out in two stages, discretization and quantization. In the discretization stage, the space of signals is partitioned into equivalence classes and quantization is carried out by replacing the signal with representative signal of the corresponding equivalence class. In thequantization stage the representative signal values are approximated by values from a finite set.The Nyquist–Shannon sampling theorem states that a signal can be exactly reconstructed from its samples if the sampling frequency is greater than twice the highest frequency of the signal; but requires an infinite number of samples . In practice, the sampling frequency is often significantly more than twice that required by the signal's limited bandwidth.A digital-to-analog converter is used to convert the digital signal back to analog. The use of a digital computer is a key ingredient in digital control systems.4. Time and space domainsMain article: Time domainThe most common processing approach in the time or space domain is enhancement of the input signal through a method called filtering. Digital filtering generally consists of some linear transformation of a number of surrounding samples around the current sample of the input or output signal. There are various ways to characterize filters; for example:∙ A "linear" filter is a linear transformation of input samples; other filters are "non-linear". Linear filters satisfy the superposition condition, i.e. if an input is a weighted linear combination of different signals, the output is an equally weighted linear combination of the corresponding output signals.∙ A "causal" filter uses only previous samples of the input or output signals; while a "non-causal" filter uses future input samples. A non-causal filter can usually be changed into a causal filter by adding a delay to it.∙ A "time-invariant" filter has constant properties over time; other filters such as adaptive filters change in time.∙Some filters are "stable", others are "unstable". A stable filter produces an output that converges to a constant value with time, or remains bounded within a finite interval. An unstable filter can produce an output that grows without bounds, with bounded or even zero input.A "finite impulse response" (FIR) filter uses only the input signals, while an "infinite impulse response" filter (IIR) uses both the input signal and previous samples of the output signal. FIR filters are always stable, while IIR filters may be unstable.Filters can be represented by block diagrams which can then be used to derive a sample processing algorithm to implement the filter using hardware instructions. A filter may also be described as a difference equation, a collection of zeroes and poles or, if it is an FIR filter, an impulse response or step response.The output of a digital filter to any given input may be calculated by convolving the input signal with the impulse response.5. Frequency domainMain article: Frequency domainSignals are converted from time or space domain to the frequency domain usually through the Fourier transform. The Fourier transform converts the signal information to a magnitude and phase component of each frequency. Often the Fourier transform is converted to the power spectrum, which is the magnitude of each frequency component squared.The most common purpose for analysis of signals in the frequency domain is analysis of signal properties. The engineer can study the spectrum to determine which frequencies are present in the input signal and which are missing.In addition to frequency information, phase information is often needed. This can be obtained from the Fourier transform. With some applications, how the phase varies with frequency can be a significant consideration.Filtering, particularly in non-realtime work can also be achieved by converting to the frequency domain, applying the filter and then converting back to the time domain. This is a fast, O(n log n) operation, and can give essentially any filter shape including excellent approximations to brickwall filters.There are some commonly used frequency domain transformations. For example, the cepstrum converts a signal to the frequency domain through Fourier transform, takes the logarithm, then applies another Fourier transform. This emphasizes thefrequency components with smaller magnitude while retaining the order of magnitudes of frequency components.6. Z-domain analysisWhereas analog filters are usually analysed on the s-plane; digital filters are analysed on the z-plane or z-domain in terms of z-transforms.Most filters can be described in Z-domain (a complex number superset of the frequency domain) by their transfer functions. A filter may be analysed in the z-domain by its characteristic collection of zeroes and poles.7. ApplicationsThe main applications of DSP are audio signal processing, audio compression, digital image processing, video compression, speech processing, speech recognition, digital communications, RADAR, SONAR, seismology, and biomedicine. Specific examples are speech compression and transmission in digital mobile phones, room matching equalization of sound in Hifi and sound reinforcement applications, weather forecasting, economic forecasting, seismic data processing, analysis and control of industrial processes, computer-generated animations in movies, medical imaging such as CAT scans and MRI, MP3 compression, image manipulation, high fidelity loudspeaker crossovers and equalization, and audio effects for use with electric guitar amplifiers8. ImplementationDigital signal processing is often implemented using specialised microprocessors such as the DSP56000, the TMS320, or the SHARC. These often process data using fixed-point arithmetic, although some versions are available which use floating point arithmetic and are more powerful. For faster applications FPGAs[3]might be used. Beginning in 2007, multicore implementations of DSPs have started to emerge from companies including Freescale and Stream Processors, Inc. For faster applications with vast usage, ASICs might be designed specifically. For slow applications, a traditional slower processor such as a microcontroller may be adequate. Also a growing number of DSP applications are now being implemented on Embedded Systems using powerful PCs with a Multi-core processor.信号处理信号处理是电气工程和应用数学领域,在离散的或连续的时间域处理和分析信号,以对这些信号进行所需的有用的操作。
FIR和IIR数字滤波器的设计摘要:随着现代计算机技术在滤波问题上的飞跃,派生出一个全新的分支——数字滤波器。
数字信号处理在科学和工程技术许多领域中得到广泛的应用,利用可编程逻辑器件和EDA技术,使用FPGA来实现FIR滤波器,可以同时兼顾实时性和灵活性。
与FIR数字滤波器相比,IIR数字滤波器可以用较低的阶数获得较高的选择性,采用一种基于FPGA的IIR数字滤波器的设计方案,首先分析了IIR数字滤波器的原理及设计方法,然后通过QuartusⅡ的设计平台,采用自顶向下的模块化设计思想将整个IIR数字滤波器分为:时序控制、延时、补码乘加和累加四个功能模块。
分别对各模块采用VHDL进行描述后,进行了仿真和综合。
关键字: FPGA;IIR数字滤波器;FIR数字滤波器;QuartusⅡ1.前言数字滤波器是用数字运算的方法完成滤波作用的一种器件,它是数字信号处理的主要技术之一。
数字滤波器可以完成模拟滤波器相同的功能,而在模拟滤波器实现困难或无法做到的场合下它更显示出优越性。
此外,数字滤波器还具有重要的工程优点,如它具有很高的精度和稳定性,特别容易复制,复制后性能完全一致,并且同一硬件可以时分多路复用或完成多频带滤波,大大减少了硬件的数量。
数字滤波器还具有较大的灵活性,转移函数容易改变,因而适应性强,尤其是随着大规模积成电路的发展,硬件可以制成标准组件,使用就更加经济、方便。
数字滤波器一般可分为两大类:即无限冲击响应(IIR)数字滤波器和有限冲击响应(FIR)数字滤波器。
IIR数字滤波器的设计一般有三种方法:即双线性Z变换法、阶跃不变法和冲击不变法。
其中双线性Z变换法最好,它可以得到与参考模拟滤波器相似的频率响应,而设计步骤较为简单。
FIR数字滤波器的设计一般有二种方法,最基本的方法就是傅立叶级数加窗口的设计方法,另一种就是计算机辅助设计方法。
前一种方法的优点是简单,缺点是设计结果不够理想,后一种方法是根据最小误差准则由计算机完成的最佳设计,但较为复杂。
IIR滤波器的原理与设计方法IIR(Infinite Impulse Response)滤波器是一种数字滤波器,其具有无限冲激响应的特点。
与FIR(Finite Impulse Response)滤波器相比,IIR滤波器具有更高的效率和更窄的频带特性。
本文将介绍IIR滤波器的原理和设计方法。
一、IIR滤波器的原理IIR滤波器是通过对输入信号和输出信号之间的差异进行递归运算而实现滤波的。
其核心原理是利用差分方程来描述滤波器的行为。
IIR滤波器可以被表达为如下形式:y[n] = b₀x[n] + b₁x[n-1] + ... + bₘx[n-ₘ] - a₁y[n-1] - ... - aₘy[n-ₘ]其中,x[n]表示输入信号的当前采样值,y[n]表示输出信号的当前采样值,a₁,...,aₘ和b₀,...,bₘ是滤波器的系数。
二、IIR滤波器的设计方法设计IIR滤波器需要确定滤波器的阶数、截止频率和系数等参数,以下介绍一种常用的设计方法:巴特沃斯滤波器设计方法。
1. 确定滤波器阶数滤波器的阶数决定了滤波器的复杂度和频率响应的形状。
阶数越高,频率响应越陡峭。
根据需要的滤波效果和计算复杂度,选择适当的滤波器阶数。
2. 确定截止频率截止频率是滤波器在频域上的边界,用于确定滤波器的通带和阻带。
根据信号的频谱分析以及滤波器的应用要求,确定合适的截止频率。
3. 求解滤波器系数根据巴特沃斯滤波器的设计方法,可以采用双线性变换、频率抽样和极点放置等技术求解滤波器的系数。
具体方法比较复杂,需要使用专业的滤波器设计软件或者数字信号处理工具包进行计算。
4. 评估设计结果设计完成后,需要评估滤波器的性能指标,如频率响应、相位响应、群延迟等。
可以通过频域分析和时域仿真等方法来评估滤波器的设计效果。
三、结论IIR滤波器是一种常用的数字滤波器,其具有无限冲激响应的特点。
通过对输入信号和输出信号进行递归运算,可以实现滤波效果。
设计IIR滤波器需要确定滤波器的阶数、截止频率和系数等参数,并通过专业的设计方法进行求解。
英文原文The simulation and the realization of the digital filterWith the information age and the advent of the digital world, digital signal processing has become one of today's most important disciplines and door technology. Digital signal processing in communications, voice, images, automatic control, radar, military, aerospace, medical and household appliances, and many other fields widely applied. In the digital signal processing applications, the digital filter is important and has been widely applied.1、figures Unit on :Analog and digital filtersIn signal processing, the function of a filter is to remove unwanted parts of the signal, such as random noise, or to extract useful parts of the signal, such as the components lying within a certain frequency range.The following block diagram illustrates the basic idea.There are two main kinds of filter, analog and digital. They are quite different in their physical makeup and in how they work. An analog filter uses analog electronic circuits made up from components such as resistors, capacitors and op amps to produce the required filtering effect. Such filter circuits are widely used in such applications as noise reduction, video signal enhancement, graphic equalisers in hi-fi systems, and many other areas. There are well-established standard techniques for designing an analog filter circuit for a given requirement. At all stages, the signal being filtered is an electrical voltage or current which is the direct analogue of the physical quantity (e.g. a sound or video signal or transducer output) involved. A digital filter uses a digital processor to perform numerical calculations on sampled values of the signal. The processor may be a general-purpose computer such as a PC, or a specialised DSP (Digital Signal Processor) chip. The analog input signal must first be sampled and digitised using an ADC (analog to digital converter). The resulting binary numbers, representing successive sampled values of the input signal, are transferred to the processor,which carries out numerical calculations on them. These calculations typically involve multiplying the input values by constants and adding the products together. If necessary, the results of these calculations, which now represent sampled values of the filtered signal, are output through a DAC (digital to analog converter) to convert the signal back to analog form.Note that in a digital filter, the signal is represented by a sequence of numbers, rather than a voltage or current.The following diagram shows the basic setup of such a system.Unit refers to the input signals used to filter hardware or software. If the filter input, output signals are separated, they are bound to respond to the impact of the Unit is separated, such as digital filters filter definition. Digital filter function, which was to import sequences X transformation into export operations through a series Y.According to figures filter function 24-hour live response characteristics, digital filters can be divided into two, namely, unlimited long live long live the corresponding IIR filter and the limited response to FIR filters. IIR filters have the advantage of the digital filter design can use simulation results, and simulation filter design of a large number of tables may facilitate simple. It is the shortcomings of the nonlinear phase; Linear phase if required, will use the entire network phase-correction. Image processing and transmission of data collection is required with linear phase filters identity. And FIR linear phase digital filter to achieve, but an arbitrary margin characteristics. Impact from the digital filter response of the units can be divided into two broad categories : the impact of the limited response (FIR) filters, and unlimited number of shocks to (IIR) digital filters.FIR filters can be strictly linear phase, but because the system FIR filter function extremity fixed at the original point, it can only use the higher number of bands to achieve their high selectivity for the same filter design indicators FIR filter called band than a few high-IIR 5-10 times, the cost is higher, Signal delay is also larger. But if the same linear phase, IIR filters must be network-wide calibration phase, the same section also increase the number of filters and network complexity. FIR filters can be used to achieve non-Digui way, not in a limited precision of a shock, and into the homes and quantitative factors of uncertainty arising from the impact of errors than IIR filter small number, and FIR filter can be used FFT algorithms, the computational speed. But unlike IIR filter can filter through the simulation results, there is no ready-made formula FIR filter must use computer-aided design software (such as MATLAB) to calculate. So, a broader application of FIR filters, and IIR filters are not very strict requirements on occasions.Unit from sub-functions can be divided into the following four categories :(1) Low-filter (LPF);(2) high-filter (HPF);(3) belt-filter (BPF);(4) to prevent filter (BSF).The following chart dotted line for the ideals of the filter frequency characteristics :A1(f) A2(f)10 f2cf 0 f2cf(a) (b)A3(f) A4(f)0 f1c f2cf 0 f1cf2cf(c) (d)(a)LPF (b)HPF (c)BPF (d)BSF2、MATLAB introducedMATLAB is a matrix laboratory (Matrix Laboratory) is intended. In addition to an excellent value calculation capability, it also provides professional symbols terms, word processing, visualization modeling, simulation and real-time control functions. MATLAB as the world's top mathematical software applications, with a strong engineering computing, algorithms research, engineering drawings, applications development, data analysis and dynamic simulation, and other functions, in aerospace, mechanical manufacturing and construction fields playing an increasingly important role. And the C language function rich, the use of flexibility, high-efficiency goals procedures. High language both advantages as well as low level language features. Therefore, C language is the most widely used programming language. Although MATLAB is a complete, fully functional programming environment, but in some cases, data and procedures with the external environment of the world is very necessary and useful. Filter design using Matlab, could be adjusted with the design requirements and filter characteristics of the parameters, visual simple, greatly reducing the workload for the filter design optimization.In the electricity system protection and secondary computer control, many signal processing and analysis are based on are certain types Yeroskipou and the second harmonics of the system voltage and current signals (especially at D process), are mixed with a variety of complex components, the filter has been installed power system during the critical components. Current computer protection and the introduction of two digital signal processing software main filter. Digital filter design using traditional cumbersome formula, the need to change the parameters after recalculation, especially in high filters, filter design workload. Uses MATLAB signal processing boxes can achieve rapid and effective digital filter design and simulation.MATLAB is the basic unit of data matrix, with its directives Biaodashi mathematics, engineering, commonly used form is very similar, it is used to solve a problem than in MATLAB C, Fortran and other languages End precision much the same thing. The popular MATLAB 5.3/Simulink3.0 including hundreds of internal function with the main pack and 30types of tool kits (Toolbox). kits can be divided into functional tool kits and disciplines toolkit. MATLAB tool kit used to expand the functional symbols terms, visualization simulation modelling, word processing and real-time control functions. professional disciplines toolkit is a stronger tool kits, tool kits control, signal processing tool kit, tool kits, etc. belonging to such communicationsMATLAB users to open widely welcomed. In addition to the internal function, all the packages MATLAB tool kits are readable document and the document could be amended, modified or users through Yuanchengxu the construction of new procedures to prepare themselves for kits.3、Digital filter designDigital filter design of the basic requirementsDigital filter design must go through three steps :(1) Identification of indicators : In the design of a filter, there must be some indicators. These indicators should be determined on the basis of the application. In many practical applications, digital filters are often used to achieve the frequency operation. Therefore, indicators in the form of general jurisdiction given frequency range and phase response. Margins key indicators given in two ways. The first is absolute indicators. It provides a function to respond to the demands of the general application of FIR filter design. The second indicator is the relative indicators. Its value in the form of answers to decibels. In engineering practice, the most popular of such indicators. For phase response indicators forms, usually in the hope that the system with a linear phase frequency bands human. Using linear phase filter design with the following response to the indicators strengths:①it only contains a few algorithms, no plural operations;②there is delay distortion, only a fixed amount of delay; ③the filter length N (number of bands for N-1), the volume calculation for N/2 magnitude.(2) Model approach : Once identified indicators can use a previous study of the basic principles and relationships, a filter model to be closer to the target system.(3) Achieved : the results of the above two filters, usually by differential equations, system function or pulse response to describe. According to this description of hardware or software used to achieve it.4、Introduced FPGAProgrammable logic device is a generic logic can use a variety of chips, which is to achieve ASIC ASIC (Application Specific Integrated Circuit) semi-customized device, Its emergence and development of electronic systems designers use CAD tools to design their own laboratory in the ASIC device. Especially FPGA (Field Programmable Gate Array) generated and development, as a microprocessor, memory, the figures for electronic system design and set a new industry standard (that is based on standard product sales catalogue in the market to buy). Is a digital system for microprocessors, memories, FPGA or three standard building blocks constitute their integration direction.Digital circuit design using FPGA devices, can not only simplify the design process and can reduce the size and cost of the entire system, increasing system reliability. They do not need to spend the traditional sense a lot of time and effort required to create integrated circuits, to avoid the investment risk and become the fastest-growing industries of electronic devices group. Digital circuit design system FPGA devices using the following main advantages(1)Design flexibleUse FPGA devices may not in the standard series device logic functional limitations. And changes in system design and the use of logic in any one stage of the process, and only through the use of re-programming the FPGA device can be completed, the system design provides for great flexibility.(2) Increased functional densityFunctional density in a given space refers to the number of functional integration logic. Programmable logic chip components doors several high, a FPGA can replace several films, film scores or even hundreds of small-scale digital IC chip illustrated in the film. FPGA devices using the chip to use digital systems in small numbers, thus reducing the number of chips used to reduce the number of printed size and printed, and will ultimately lead to a reduction in the overall size of the system.(3) Improve reliabilityPrinting plates and reduce the number of chips, not only can reduce system size, but it greatly enhanced system reliability. A higher degree of integration than systems in many low-standard integration components for the design of the same system, with much higher reliability. FPGA device used to reduce the number of chips required to achieve the system in the number printed on the cord and joints are reduced, the reliability of the system can beimproved.(4) Shortening the design cycleAs FPGA devices and the programmable flexibility, use it to design a system for longer than traditional methods greatly shortened. FPGA device master degrees high, use printed circuit layout wiring simple. At the same time, success in the prototype design, the development of advanced tools, a high degree of automation, their logic is very simple changes quickly. Therefore, the use of FPGA devices can significantly shorten the design cycle system, and speed up the pace of product into the market, improving product competitiveness.(5) Work fastFPGA/CPLD devices work fast, generally can reach several original Hertz, far larger than the DSP device. At the same time, the use of FPGA devices, the system needed to achieve circuitclasses and small, and thus the pace of work of the entire system will be improved.(6) Increased system performance confidentialityMany FPGA devices have encryption functions in the system widely used FPGA devices can effectively prevent illegal copying products were others(7) To reduce costsFPGA device used to achieve digital system design, if only device itself into the price, sometimes you would not know it advantages, but there are many factors affecting the cost of the system, taken together, the cost advantages of using FPGA is obvious. First, the use of FPGA devices designed to facilitate change, shorten design cycles, reduce development costs for system development; Secondly, the size and FPGA devices allow automation needs plug-ins, reducing the manufacturing system to lower costs; Again, the use of FPGA devices can enhance system reliability, reduced maintenance workload, thereby lowering the cost of maintenance services for the system. In short, the use of FPGA devices for system design to save costs.FPGA design principles :FPGA design an important guiding principles : the balance and size and speed of exchange, the principles behind the design of the filter expression of a large number of certification.Here, "area" means a design exertion FPGA/CPLD logic resources of the FPGA can be used to the typical consumption (FF) and the search table (IUT) to measure more general measure can be used to design logic equivalence occupied by the door is measured. "pace"means stability operations in the chip design can achieve the highest frequency, the frequency of the time series design situation, and design to meet the clock cycle -- PADto pad, Clock Setup Time, Clock Hold Beijing, Clock-to-Output Delay, and other characteristics of many time series closely related. Area (area) and speed (speed) runs through the two targets FPGA design always is the ultimate design quality evaluation criteria. On the size and speed of the two basic concepts : balance of size and speed and size and speed of swap.One pair of size and speed is the unity of opposites contradictions body. Requirements for the design of a design while the smallest, highest frequency of operation is unrealistic. More scientific goal should be to meet the design requirements of the design time series (includes requirements for the design frequency) premise, the smallest chip area occupied. Or in the specified area, the design time series cushion greater frequency run higher. This fully embodies the goals of both size and speed balanced thinking. On the size and speed requirements should not be simply interpreted as raising the level and design engineers perfect sexual pursuit, and should recognize that they are products and the quality and cost of direct relevance. If time series cushion larger design, running relatively high frequency, that the design Jianzhuangxing stronger, more quality assurance system as a whole; On the other hand, the smaller size of consumption design is meant to achieve in chip unit more functional modules, the chip needs fewer, the entire system has been significantly reduced cost. As a contradiction of the two components, the size and speed is not the same status. In contrast, meet the timetables and work is more important for some frequency when both conflicts, the use of priority guidelines.Area and the exchange rate is an important FPGA design ideas. Theoretically, if a design time series cushion larger, can run much higher than the frequency design requirements, then we can through the use of functional modules to reduce the consumption of the entire chip design area, which is used for space savings advantages of speed; Conversely, if the design of a time series demanding, less than ordinary methods of design frequency then generally flow through the string and data conversion, parallel reproduction of operational module, designed to take on the whole "string and conversion" and operate in the export module to chip in the data "and string conversion" from the macro point of view the whole chip meets the requirements of processing speed, which is equivalent to the area of reproduction - rate increase.For example. Assuming that the digital signal processing system is 350Mb/s input data flow rate, and in FPGA design, data processing modules for maximum processing speed of150Mb/s, because the data throughput processing module failed to meet requirements, it is impossible to achieve directly in the FPGA. Such circumstances, they should use "area-velocity" thinking, at least three processing modules from the first data sets will be imported and converted, and then use these three modules parallel processing of data distribution, then the results "and string conversion," we have complete data rate requirements. We look at both ends of the processing modules, data rate is 350Mb/s, and in view of the internal FPGA, each sub-module handles the data rate is 150Mb/s, in fact, all the data throughput is dependent on three security modules parallel processing subsidiary completed, that is used by more chip area achieve high-speed processing through "the area of reproduction for processing speed enhancement" and achieved design.FPGA is the English abbreviation Field of Programmable Gate Array for the site programmable gate array, which is in Pal, Gal, Epld, programmable device basis to further develop the product. It is as ASIC (ASIC) in the field of a semi-customized circuit and the emergence of both a customized solution to the shortage circuit, but overcome the original programmable devices doors circuit few limited shortcomings.FPGA logic module array adopted home (Logic Cell Array), a new concept of internal logic modules may include CLB (Configurable Logic Block), export import module IOB (Input Output Block) and internal links (Interconnect) 3. FPGA basic features are :(1) Using FPGA ASIC design ASIC using FPGA circuits, the chip can be used,while users do not need to vote films production.(2) FPGA do other customized or semi-customized ASIC circuits throughout the Chinese specimen films.3) FPGA internal capability and rich I/O Yinjue.4) FPGA is the ASIC design cycle, the shortest circuit, the lowest development costs, risks among the smallest device5) FPGA using high-speed Chmos crafts, low consumption, with CMOS, TTL low-power compatibleIt can be said that the FPGA chip is for small-scale systems to improve system integration, reliability one of the bestCurrently FPGA many varieties, the Revenue software series, TI companies TPC series, the fiex ALTERA company seriesFPGA is stored in films from the internal RAM procedures for the establishment of the state of its work, therefore, need to programmed the internal Ram. Depending on the different configuration, users can use a different programming methodsPlus electricity, FPGA, EPROM chips will be read into the film, programming RAM中data, configuration is completed, FPGA into working order. Diaodian, FPGA resume into white films, the internal logic of relations disappear, FPGA to repeated use. FPGA's programming is dedicated FPGA programming tool, using generic EPROM, prom programming device can. When the need to modify functional FPGA, EPROM can only change is. Thus, with a FPGA, different programming data to produce different circuit functions. Therefore, the use of FPGA very flexible.There are a variety of FPGA model : the main model for a parallel FPGA plus a EPROM manner; From the model can support a number of films FPGA; serial prom programming model could be used serial prom FPGA programming FPGA; The external model can be engineered as microprocessors from its programming microprocessors.Verilog HDL is a hardware description language for the algorithm level, doors at the level of abstract level to switch-level digital system design modelling. Modelling of the target figure by the complexity of the system can be something simple doors and integrity of electronic digital systems. Digital system to the levels described, and in the same manner described in Hin-time series modelling.Verilog HDL language with the following description of capacity : design behaviour characteristics, design data flow characteristics, composition and structure designed to control and contain the transmission and waveform design a certification mechanism. All this with the use of a modelling language. In addition, Verilog HDL language programming language interface provided by the interface in simulation, design certification from the external design of the visit, including specific simulation control and operation.Verilog HDL language grammar is not only a definition, but the definition of each grammar structure are clear simulation, simulation exercises. Therefore, the use of such language to use Verilog simulation models prepared by a certification. From the C programming language, the language inherited multiple operating sites and structures. Verilog HDL provides modelling capacity expansion, many of the initial expansion would be difficult to understand. However, the core subsets of Verilog HDL language very easy to learn and use, which is sufficient formost modelling applications. Of course, the integrity of the hardware description language is the most complex chips from the integrity of the electronic systems described.historyVerilog HDL language initially in 1983 by Gateway Design Automation companies for product development simulator hardware modelling language. Then it is only a dedicated language. Since their simulation, simulation devices widely used products, Verilog HDL as a user-friendly and practical language for many designers gradually accepted. In an effort to increase the popularity of the language activities, Verilog HDL language in 1990 was a public area. Open Verilog International (OVI) is to promote the development of Verilog international organizations. 1992, decided to promote OVI OVI standards as IEEE Verilog standards. The effort will ultimately succeed, a IEEE1995 Verilog language standard, known as IEEE Std 1364-1995. Integrity standards in Verilog hardware description language reference manual contains a detailed description.Main capacity:Listed below are the main Verilog hardware description language ability*Basic logic gate, and, for example, or have embedded in the language and nand* Users of the original definition of the term (UDP), the flexibility. Users can be defined in the original language combinations logic original language, the original language of logic could also be time series* Switches class infrastructure models, such as the nmos and pmos also be embedded in the language* Hin-language structure designated for the cost of printing the design and trails Shi Shi and design time series checks.* Available three different ways to design or mixed mode modelling. These methods include : acts described ways - use process of structural modelling; Data flow approach - use of a modelling approach Fuzhi expression; Structured way - using examples of words to describe modular doors and modelling.* Verilog HDL has two types of data : data types and sequence data line network types. Line network types that the physical links between components and sequence types that abstract data storage components.* To describe the level design, the structure can be used to describe any level module example* Design size can be arbitrary; Language is design size (size) impose any restrictions* Verilog HDL is no longer the exclusive language of certain companies but IEEE standards.* And the machine can read Verilog language, it may as EDA tools and languages of the world between the designers* Verilog HDL language to describe capacity through the use of programming language interface (PLI) mechanism further expansion. PLI is to allow external functions of the visit Verilog module information, allowing designers and simulator world Licheng assembly* Design to be described at a number of levels, from the switch level, doors level, register transfer level (RTL) to the algorithm level, including the level of process and content* To use embedded switching level of the original language in class switch design integrity modelling* Same language can be used to generate simulated incentive and certification by the designated testing conditions, such as the value of imports of the designated*Verilog HDL simulation to monitor the implementation of certification, the certification process of implementing the simulation can be designed to monitor and demonstrate value. These values can be used to compare with the expectations that are not matched in the case of print news reports.* Acts described in the class, not only in the RTL level Verilog HDL design description, and to describe their level architecture design algorithm level behavioural description* Examples can use doors and modular structure of language in a class structure described* Verilog HDL mixed mode modelling capabilities in the design of a different design in each module can level modelling* Verilog HDL has built-in logic function, such as*Structure of high-level programming languages, such as conditions of expression, and the cycle of expression language, language can be used* To it and can display regular modelling* Provide a powerful document literacy* Language in the specific circumstances of non-certainty that in the simulator, different models can produce different results; For example, describing events in the standard sequence of events is not defined.5、In troduction of DSPToday, DSP is w idely used in the modern techno logy and it has been the key part of many p roducts and p layed more and mo re impo rtant ro le in our daily life.Recent ly, Northw estern Po lytechnica lUniversity Aviation Microelect ronic Center has comp leted the design of digital signal signal p rocesso r co re NDSP25, w h ich is aim ing at TM S320C25 digital signal p rocesso r of Texas Inst rument TM S320 series. By using top 2dow n design flow , NDSP25 is compat ible w ith inst ruct ion and interface t im ing of TM S320C25.Digital signal processors (DSP) is a fit for real-time digital signal processing for high-speed dedicated processors, the main variety used for real-time digital signal processing to achieve rapid algorithms. In today's digital age background, the DSP has become the communications, computer, and consumer electronics products, and other fields based device.Digital signal processors and digital signal processing is inseparably, we usually say "DSP" can also mean the digital signal processing (Digital Signal Processing), is that in this digital signal processors Lane. Digital signal processing is a cover many disciplines applied to many areas and disciplines, refers to the use of computers or specialized processing equipment, the signals in digital form for the collection, conversion, recovery, valuation, enhancement, compression, identification, processing, the signals are compliant form. Digital signal processors for digital signal processing devices, it is accompanied by a digital signal processing to produce. DSP development process is broadly divided into three phases : the 20th century to the 1970s theory that the 1980s and 1990s for the development of products. Before the emergence of the digital signal processing in the DSP can only rely on microprocessors (MPU) to complete. However, the advantage of lower high-speed real-time processing can not meet the requirements. Therefore, until the 1970s, a talent made based DSP theory and algorithms. With LSI technology development in 1982 was the first recipient of the world gave birth to the DSP chip. Years later, the second generation based on CMOS工艺DSP chips have emerged. The late 1980s, the advent of the third generation of DSP chips. DSP is the fastest-growing 1990s, there have been four successive five-generation and the generation DSP devices. After 20 years of development, the application of DSP products has been extended to people's learning, work and all aspects of life and gradually become electronics products determinants.。
IIRDigitaFilterDesignAn important step in the development of a digital filter is the determination of a realizable transfer function G(z) approximating the given frequency response specifications. If an IIR filter is desired,it is also necessary to ensure that G(z) is stable. The process of deriving the transfer function G(z) is called digital filter design. After G(z) has been obtained, the next step is to realize it in the form of a suitable filter structure. In chapter 8,we outlined a variety of basic structures for the realization of FIR and IIR transfer functions. In this chapter,we consider the IIR digital filter design problem. The design of FIR digital filters is treated in chapter 10.First we review some of the issues associated with the filter design problem.A widely used approach to IIR filter design based on the conversion of a prototype analog transfer function to a digital transfer function is discussed next. Typical design examples are included to illustrate this approach. We then consider the transformation of one type of IIR filter transfer function into another type, which is achieved by replacing the complex variable z by a function of z. Four commonly used transformations are summarized. Finally we consider the computer-aided design of IIR digital filter. To this end, we restrict our discussion to the use of matlab in determining the transfer functions.preliminary considerationsThere are two major issues that need to be answered before one can develop thedigital transfer function G(z). The first and foremost issue is the development of a reasonable filter frequency response specification from the requirements of the overall system in which the digital filter is to be employed. The second issue is to determine whether an FIR or IIR digital filter is to be designed. In the section ,we examine these two issues first . Next we review the basic analytical approach to the design of IIR digital filters and then consider the determination of the filter order that meets the prescribed specifications. We also discuss appropriate scaling of the transfer function.9.1.1 Digital Filter SpecificationsAs in the case of the analog filter,either the magnitude and/or the phase(delay) response is specified for the design of a digital filter for most applications. In some situations, the unit sample response or step response may be specified. In most practical applications, the problem of interest is the development of a realizable approximation to a given magnitude response specification. As indicated in section 4.6.3, the phase response of the designed filter can be corrected by cascading it with an allpass section. The design of allpass phase equalizers has received a fair amount of attention in the last few years.We restrict our attention in this chapter to the magnitude approximation problem only. We pointed out in section 4.4.1 that there are four basic types of filters,whose magnitude responses are shown in Figure . Since the impulse response corresponding to each of these is noncausal and of infinite length, these ideal filters are not realizable. One way of developing a realizable approximation to these filter would be to truncate the impulse response as indicated in Eq. for a lowpass filter. Themagnitude response of the FIR lowpass filter obtained by truncating the impulse response of the ideal lowpass filter does not have a sharp transition from passband to stopband but, rather, exhibits a gradual "roll-off."Thus, as in the case of the analog filter design problem outlined in section5.4.1, the magnitude response specifications of a digital filter in the passband and in the stopband are given with some acceptable tolerances. In addition, a transition band is specified between the passband and the stopband to permit the magnitude to drop off smoothly. For example, the magnitude )(ωj e G of a lowpass filter may be given as shown in Figure . As indicated in the figure, in the passband defined by 0p ωω≤≤, we require that the magnitude approximates unity with an error of p δ±,., p p j p for e G ωωδδω≤+≤≤-,1)(1.In the stopband, defined by πωω≤≤s ,we require that the magnitude approximates zero with an error of i s ,δ.e., ,)(s j e G δω≤ for πωω≤≤s .The frequencies p ω and s ω are , respectively, called the passband edge frequency and the stopband edge frequency. The limits of the tolerances in the passband and stopband, p δ and s δ, are usually called the peak ripple values. Note that thefrequency response )(ωj e G of a digital filter is a periodic function of ω,and themagnitude response of a real-coefficient digital filter is an even function of ω. As a result, the digital filter specifications are given only for the range πω≤≤0.Digital filter specifications are often given in terms of the loss function,)(log 20)(10ωωζj e G -=, in dB. Here the peak passband ripple p α and the minimum stopband attenuation s α are given in dB,., the loss specifications of a digital filter are given bydB p p )1(log 2010δα--=,dB s s )(log 2010δα-=.Preliminary ConsiderationsAs in the case of an analog lowpass filter, the specifications for a digital lowpass filter may alternatively be given in terms of its magnitude response, as in Figure . Here the maximum value of the magnitude in the passband is assumed to be unity, and the maximum passband deviation, denoted as 1/21ε+,is given by the minimum value of the magnitude in the passband. The maximum stopband magnitude is denoted by 1/A.For the normalized specification, the maximum value of the gain function or the minimum value of the loss function is therefore 0 dB. The quantity max α given bydB )1(log 20210max εα+=Is called the maximum passband attenuation. For p δ<<1, as is typically the case, it can be shown thatp p αδα2)21(log 2010max ≅--≅The passband and stopband edge frequencies, in most applications, are specified in Hz, along with the sampling rate of the digital filter. Since all filterdesign techniques are developed in terms of normalized angular frequencies p ω and s ω,the sepcified critical frequencies need to be normalized before a specific filter design algorithm can be applied. Let T F denote the sampling frequency in Hz, and F P and F s denote, respectively,the passband and stopband edge frequencies in Hz. Then the normalized angular edge frequencies in radians are given byT F F F F p Tp T p p ππω22==Ω=T F F F F s Ts T s s ππω22==Ω= 9.1.2 Selection of the Filter Type The second issue of interest is the selection of the digital filter type,.,whether an IIR or an FIR digital filter is to be employed. The objective of digital filter design is to develop a causal transfer function H(z) meeting the frequency response specifications. For IIR digital filter design, the IIR transfer function is a real rational function of 1-z . H(z)=N MdNzz d z d d pMz z p z p p ------++++++++......2211022110 Moreover, H(z) must be a stable transfer function, and for reduced computational complexity, it must be of lowest order N. On the other hand, for FIR filter design, the FIR transfer function is a polynomial in 1-z :∑=-=N n n zn h z H 0][)(For reduced computational complexity, the degree N of H(z) must be as small as possible. In addition, if a linear phase is desired, then the FIR filter coefficients must satisfy the constraint:][][N n h n h -±=T here are several advantages in using an FIR filter, since it can be designed with exact linear phase and the filter structure is always stable with quantized filter coefficients. However, in most cases, the order N FIR of an FIR filter is considerably higher than the order N IIR of an equivalent IIR filter meeting the same magnitude specifications. In general, the implementation of the FIR filter requires approximately N FIR multiplications per output sample, whereas the IIR filter requires 2N IIR +1 multiplications per output sample. In the former case, if the FIR filter is designed with a linear phase, then the number of multiplications per output sample reduces to approximately (N FIR+1)/2. Likewise, most IIR filter designs result in transfer functions with zeros on the unit circle, and the cascade realization ofN with all of the zeros on the unit circle requires an IIR filter of orderIIRN+3)/2] multiplications per output sample. It has been shown that for most [(3IIRpractical filter specifications, the ratio N FIR/N IIR is typically of the order of tens or more and, as a result, the IIR filter usually is computationally more efficient[Rab75]. However ,if the group delay of the IIR filter is equalized by cascading it with an allpass equalizer, then the savings in computation may no longer be that significant [Rab75]. In many applications, the linearity of the phase response of the digital filter is not an issue,making the IIR filter preferable because of the lower computational requirements.9.1.3 Basic Approaches to Digital Filter DesignIn the case of IIR filter design, the most common practice is to convert the digital filter specifications into analog lowpass prototype filter specifications, and then to transform it into the desired digital filter transfer function G(z).This approach has been widely used for many reasons:(a) Analog approximation techniques are highly advanced.(b) They usually yield closed-form solutions.(c) Extensive tables are available for analog filter design.(d) Many applications require the digital simulation of analog filters.In the sequel, we denote an analog transfer function as )()()(s D s P s H a a a =, Where the subscript "a" specifically indicates the analog domain. The digital transfer function derived form H a (s) is denoted by)()()(z D z P z G = The basic idea behind the conversion of an analog prototype transfer function H a (s) into a digital IIR transfer function G(z) is to apply a mapping from the s-domain to the z-domain so that the essential properties of the analog frequency response are preserved. The implies that the mapping function should be such that(a) The imaginary(j Ω) axis in the s-plane be mapped onto the circle of the z-plane.(b) A stable analog transfer function be transformed into a stable digital transfer function.To this end,the most widely used transformation is the bilinear transformation described in Section .Unlike IIR digital filter design,the FIR filter design does not have any connection with the design of analog filters. The design of FIR filter design does not have any connection with the design of analog filters. The design of FIR filtersis therefore based on a direct approximation of the specified magnitude response,with the often added requirement that the phase response be linear. As pointed out in Eq., a causal FIR transfer function H(z) of length N+1 is a polynomial in z -1 of degree N. The corresponding frequency response is given by∑=-=N n n j j en h e H 0][)(ωω.It has been shown in Section 3.2.1 that any finite duration sequence x[n] of length N+1 is completely characterized by N+1 samples of its discrete-time Fourier transfer X(ωj e ). As a result, the design of an FIR filter of length N+1 may be accomplished by finding either the impulse response sequence {h[n]} or N+1 samples of its frequency response )H(e j ω. Also, to ensure a linear-phase design, the condition of Eq. must be satisfied. Two direct approaches to the design of FIR filters are the windowed Fourier series approach and the frequency sampling approach. We describe the former approach in Section . The second approach is treated in Problem . In Section we outline computer-based digital filter design methods.作者:Sanjit国籍:USA出处:Digital Signal Processing -A Computer-Based Approach 3eIIR数字滤波器的设计在一个数字滤波器发展的重要步骤是可实现的传递函数G(z)的接近给定的频率响应规格。