Reflections Function Method In the X-Ray Reflectometry

Low Power Design with CoolRunner-II CPLDsXAPP377 (v1.0) May 8, 2002It may be possible to avoid using shunt termination resistors by using a very short transmission line. The rule of thumb for a short transmission line is one whose length is less than one-sixth the electrical length of the rise time, and is described using the following equation:where:•Length = maximum line length in inches•T rise = rise time in seconds•L = the line inductance in Henries/inch• C = the line capacitance in Farads/inchBy using the CoolRunner-II CPLD slew rate feature configured to SLOW, the rise time becomes longer. Using the above equation, it can be determined if the length of the transmission line can be effectively long enough to avoid reflections altogether. If by using the SLOW slew rate feature, the length of the transmission line is short by the above rule of thumb, shunt bus termination resistors can be avoided thereby saving power.If either method is not an option, insert a series termination resistor positioned at the source pin with the same value as the transmission line impedance. This option will avoid excessive power consumption (since there is no shunt load) and eliminate reflections at the source. However, a series termination resistor will allow one reflection at the load (since the load impedance does not match the transmission line impedance) which implies that any component mid way between the source and the load will see two transitions: the incident wave and the single reflected wave created at the load.Reduce System VoltageUsing the total current equation with fixed capacitance and average frequency, it becomes readily apparent that reducing system voltage will reduce power consumption, provided the system voltage remains within recommended operating specifications. Therefore, it makes sense to use a 1.8V device in lieu of a 3.3V or 2.5V device. CoolRunner-II CPLDs are 1.8V devices and therefore utilize this concept. Further, a device made with a smaller process technology, such as CoolRunner-II CPLDs, will generally have lower lumped internal capacitance values thereby reaching additional power savings. Combining these two factors with reducing average system frequency will also cut power consumption.With any voltage device, there is a recommended operating range, and it may be advantageous to operate low in that voltage range to further reduce power consumption. Voltages that are outside the recommended operating range may cause excessive power consumption including adverse functional performance.Reduce Bus LoadingConnecting an external bus to a CMOS device will increase power consumption due to the loading effects of the bus on the device. The primary factor from loading is given by capacitive or resistive bus components as seen by the output buffer looking into the bus.Capacitive loading comes in two forms: lumped and distributed. Lumped capacitance is typically found from the gate of the input buffer of other connected CMOS devices. It is also developed from any capacitive element that is attached to the bus. Distributed capacitance is present due to the routing of the trace on the PCB. Both types will charge and discharge during logic transitions based on the previous logic state of the bus. Capacitive loading will draw current from the CMOS device whose output buffer is driving the bus, thereby increasing apparent power consumption of that device as seen at its power pins. To minimize power consumption based on this capacitive loading effect, it is necessary to reduce the size of the lumped capacitance found in attached devices, and to shorten the PCB traces. Doing so will also increase potential system speed since reflections are less likely.Length16--T riseLC-----------⋅«Interfacing to Mobile SDRAM with CoolRunner-II CPLDs Mobile SDRAM device. The testbench controls the initialization requirements, single read/writeoperations, and tests the power down modes of the SDRAM.VHDL Code THIRD PARTIES MAY HAVE PATENTS ON THE CODE PROVIDED. BY PROVIDING THIS CODE AS ONE POSSIBLE IMPLEMENTATION OF THIS DESIGN, XILINX IS MAKING NOREPRESENTATION THAT THE PROVIDED IMPLEMENTATION OF THIS DESIGN IS FREEFROM ANY CLAIMS OF INFRINGEMENT BY ANY THIRD PARTY. XILINX EXPRESSLYDISCLAIMS ANY WARRANTY OR CONDITIONS, EXPRESS, IMPLIED, STATUTORY OROTHERWISE, AND XILINX SPECIFICALLY DISCLAIMS ANY IMPLIED WARRANTIES OFMERCHANTABILITY, NON-INFRINGEMENT, OR FITNESS FOR A PARTICULAR PURPOSE,THE ADEQUACY OF THE IMPLEMENTATION, INCLUDING BUT NOT LIMITED TO ANYWARRANTY OR REPRESENTATION THAT THE IMPLEMENTATION IS FREE FROMCLAIMS OF ANY THIRD PARTY. FURTHERMORE, XILINX IS PROVIDING THISREFERENCE DESIGN "AS IS" AS A COURTESY TO YOU.Conclusion CoolRunner-II CPLD devices are the perfect compliment to low power Mobile SDRAM memory.These two low power devices are targeted for handheld, mobile computing applications.CoolRunner-II CPLD devices feature low power consumption and create a seamless interfaceto Mobile SDRAM memory.References 1.Micron Data Sheet. MT48V16M16LFFG 256Mb: x16 Mobile SDRAM. Micron Technology,Inc. 2002.2.Micron Technical Note. TN-48-10. Mobile SDRAM Power-Saving Features. MicronTechnology, Inc. 2002.3.Samsung Data Sheet. K4S64163LF-RG/S 4Mx16 Mobile SDRAM. Rev 1.0. SamsungElectronics 2002.AdditionalInformationCoolRunner-II Data Sheets, Application Notes, and White PapersRevision History The following table shows the revision history for this document.Date Version Revision09/23/03 1.0Initial Xilinx release.12/01/03 1.1ErrataXAPP394 (v1.1) December 1, 2003。

RLS ALGORITHM FOR ACOUSTIC ECHO CANCELLATIONAmit Munjal*, Vibha Aggarwal**, Gurpal Singh****/**RIMT-IET Mandi Gobindgarh, India,*** BBSBEC Fatehgarh Sahib, India *amit_munjal@, **vibha_ec@yahoo.co.in, ***gurpal@Abstract-Acoustic echo cancellation is a common occurrence in today’s telecommunication systems. It occurs when an audio source and sink operate in full duplex mode; an example of this is a hands-free loudspeaker telephone. In this situation the received signal is output through the telephone loudspeaker (audio source), this audio signal is then reverberated through the physical environment and picked up by the systems microphone (audio sink). The effect is the return to the distant user of time delayed and attenuated images of their original speech signal. The signal interference caused by acoustic echo is distracting to both users and causes a reduction in the quality of the communication. This paper focuses on the use of RLS algorithm to reduce this unwanted echo, thus increasing communication quality .I. INTRODUCTIONAcoustic echo occurs when an audio signal is reverberated in a real environment, resulting in the original intended signal plus attenuated, time-delayed images of this signal. This paper will focus on the occurrence of acoustic echo in telecommunication systems. Such a system consists of coupled acoustic input and output devices, both of which are active concurrently. An example of this is a hands-free telephony system. In this scenario the system has both an active loudspeaker and microphone input operating simultaneously.The system then acts as both a receiver and transmitter in full duplex mode. When a signal is received by the system, it is output through the loudspeaker into an acoustic environment. This signal is reverberated within the environment and returned to the system via the microphone input. These reverberated signals contain time-delayed images of the original signal, which are then returned to the original sender (Figure 1.1, is the attenuation, is time delay).The occurrence of acoustic echo in speech transmission causessignal interference and reduced quality of communication. Themethod used to cancel the echo signal is known as adaptive filtering.k a ktFigure 1.1: Origins of acoustic echo. Adaptive filters are dynamic filters, which iteratively alter their characteristics in order to achieve an optimal desired output. An adaptive filter algorithmically alters its parameters in order to minimize a function of the difference between the desired output its actual output . This function is known as the cost function of the adaptive algorithm. Figure 1.2 shows a block diagram of the adaptive echo cancellation system implemented throughout this paper. Here the filter represents the impulse response of the acousticenvironment, represents the adaptive filter used to cancel the echo signal. The adaptive filter aims to equate itsoutput to the desired output (the signal reverberated within the acoustic environment). At each iteration the error signal, is fed back into the filter, where the filter characteristics are altered accordingly.[1] )(n d )(n y )(n H )(n W )(n y )(n d )()()(n y n d n e −=Figure 1.2: Block diagram of an adaptive echo cancellation system. The aim of an adaptive filter is to calculate the differencebetween the desired signal and the adaptive filter output, . This error signal is fed back into the adaptive filter and its coefficients are changed algorithmically in order to minimize a function of this difference, known as the cost function. In the case of acoustic echo cancellation, the optimal output of the adaptive filter is equal in value to the unwanted echoed signal. When the adaptive filter output is equal to desired signal the error signal goes to zero. In this situation the echoed signal would be completely cancelled and the far user would not hear any of their original speech returned to them.[4])(n eII. RECURSIVE LEAST SQUARES (RLS) ALGORITHM.These algorithms attempt to minimize the cost function in equation 2.1 [2]. Where is the time at which the RLS algorithm commences and 1=k λ is a small positive constant very close to, but smaller than 1. With values of 1<λ more importance is given to the most recent error estimates and thus the more recent input samples, this results in a scheme that places more emphasis on recent samples of observed data and tends to forget the past [2].∑=−=nk n k n k e n 12)()(λζ (2.1)Unlike the LMS algorithm and its derivatives, the RLSalgorithm directly considers the values of previous error estimations. RLS algorithms are known for excellent performance when working in time varying environments. These advantages come with the cost of an increased computational complexity and some stability problems [3].A. DERIVATION OF THE RLS ALGORITHM.The RLS cost function of equation 2.1 shows that at a time n, all previous values of the estimation error since the commencement of the RLS algorithm are required. Clearly as time progresses the amount of data required to process this algorithm increases. The fact that memory and computation capabilities are limited makes the RLS algorithm a practical impossibility in its purest form. However, the derivation still assumes that all data values are processed. In practice only a finite number of previous values are considered, this number corresponds to the order of the RLS FIR filter, .N First define as the output of the FIR filter, at , using the current tap weight vector, and the input vector of a previous time . The estimation error value is the difference between the desired output value at time k, and the corresponding value of . These and other appropriatedefinitions are expressed in equation 2.2, for.)(k y n n k )(k e n )(k y n n k ,.......,3,2,1= [])()()()]()......2(),1([)()()......2(),1()()]()....2(),1([)()()()()()()(n y n d n e n e e e n e n y y y n y n d d d n d k y k d k e k x n w k y T n n n Tn n n TnnTn −====−==(2.2)If define the X (n) as the matrix consisting of the nprevious input column vector up to the present time then y (n) can also be expressed as equation 2.3.[])()()()(),......,2(),1()(n w n X n y n x x x n X T== (2.3)The cost function of equation 2.1 can then be expressed in matrix vector form using )(n Λ, a diagonal matrix consisting of the weighting factors.)()(~)()()(12n e n n e k e n T nk nk n Λ==∑=−λζ⎥⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎢⎣⎡=Λ−−−1 00...............0 (00)0 000...00)(~321n n n n λλλ(2.4)Substituting values from equations 2.2 and 2.3, the costfunction can be expanded then reduced as in equation 2.5. (Temporarily dropping (n) notation for clarity).w w w d d w X w X d w X w X d d d yy d y y d d d n e n n e n T T T T T T T T T T T T T T T T λλψθζ~~2~)(~)(~)()(~~~~~~)()(~)()(+−Λ=Λ+Λ−Λ−Λ=Λ+Λ−Λ−Λ=Λ=)()(~)()(~)()(~)()(~n d n n X n n X n n X n T Λ=Λ=λλθψ (2.5)Then derive the gradient of the above expression for thecost function with respect to the filter tap weights. By forcingthis to zero then find the coefficients for the filter,)(n w ,which minimizes the cost function.[5] )(~)(~)()(~)()(~1n n n w n n w n λλλλθψθψ−== (2.6) The matrix )(n ψ in the above equation can be expanded and then rearranged in a recursive form; then use the special form of the matrix inversion lemma of equation 2.7 to find an inverse for this matrix, which is required to calculate the tap weight vector update. The vector k (n) is known as the gain vector and is included in order to simplify the calculation.()aA a A aa A A aa A T T T 111111−−−−−+−=+ααα(2.7)))1(~)()()1(~()()1(~)(1)1(~)()()1(~)1(~)()()1(~)(~111111111111−−−=−+−−−−=+−=−−−−−−−−−−−−n n x n k n n x n n x n n x n x n n n x n x n n T T T T λλλλλλλλψψλψλψψλψλψλψ where)()(~)()1(~)(1)()1(~)(11111n x n n x n n x n x n n k T −−−−−=−+−=λλλψψλψλ (2.8) The vector )(n λθof equation 2.5 can also be expressedin a recursive form. Using this and substituting )(1n −ψfrom equation 2.8 into equation 2.6 finally arrive at the filter weightupdate vector for the RLS algorithm, as in equation2.9.)()()1()())()1()()(()1()()()1()()()1()()()1(~)1()()1(~)1(~)(~)(~)()()()1(~)(~1111n e n k n w n w n x n w n d n k n w n d n k n w n x n k n w n d n k n n x n k n n n n n w n d n x n n n T T T −−−−+−=−−+−=+−−−=+−−−−−==+−=λλλλλλλλθψθψθψθλθwhere)()1()()(1n x n w n d n e T n −−=− (2.9)C. IMPLEMENTATION OF THE RLS ALGORITHMThe memory of the RLS algorithm is confined to a finite number of values, corresponding to the order of the filter tap weight vector. Firstly, two factors of the RLS implementation should be noted: the first is that although matrix inversion is essential to the derivation of the RLS algorithm, no matrix inversion calculations are required for the implementation, thus greatly reducing the amount of computational complexity of the algorithm. Secondly, unlike the LMS based algorithms, current variables are updated within the iteration they are to be used, using values from the previous iteration.To implement the RLS algorithm, the following steps are executed in the following order.1. The filter output is calculated using the filter tap weights from the previous iteration and the current input vector.)()1()(1n x n w n y T n −=− (2.10)2. The intermediate gain vector is calculated using equation 2.11.)()()(1)()()1(~)(1n u n u n x n k n x n n u T +=−=−λψλ (2.11) 3. The estimation error value is calculated using equation 2.12.)()()(11n y n d n e n n −−−= (2.12) 4. The filter tap weight vector is updated using equation 2.12 and the gain vector calculated in equation 2.11.)()()1()(1n e n k n w n w n T −+−= (2.13)5. The inverse matrix is calculated using equation 2.14.)])1()([)()1(()(1111−×−−=−−−−n n x n k n n T λλλψψλψ (2.14)Each iteration of the RLS algorithm requiresmultiplication operations and additions [2].24N 23NIII. RESULTS OF RLS ALGORITHMThe RLS algorithm was simulated using Matlab. This algorithm proved to be very effective. Figure 3.1 shows the input signal. Figure 3.2and 3.3 shows the estimated error signal and desired signal. Figure 3.5 and 3.6 shows the impulse response of the RLS adaptive algorithm at integer multiples of 7500 iterations. Figure 3.8 shows the RLSadaptive filter echo signal attenuation.Figure 3.1: Input SignalFigure 3.2: Error SignalFigure 3.3: Desired SignalFigure 3.4: Adaptive Filter OutputFigure 3.5: Actual Impulse ResponseFigure3.6: Convergence of the RLS Adaptive Filter toActual Impulse ResponseFigure 3.7: Mean Square ErrorFigure 3.8: RLS Algorithm Echo Signal AttenuationCONCLUSIONIn RLS algorithm average attenuation is -16.4965 dB and numbers of multiplications are . It has the greatest attenuation of any algorithm, and converges much faster than the LMS algorithm. This performance comes at the cost of computational complexity and considering the large FIR order required for echo cancellation, this is not feasible for real time implementation. In future we can also perform this echo cancellation with other adaptive algorithms. 24NREFRENCES[1] Haykin, Simon. 1991, Adaptive FilterTheory. 2nd Edition. Prentice-Hall Inc., New Jersey.[2] Farhang-Boroujeny, B. 1999, Adaptive Filters, Theory and Applications. John Wiley and Sons, New York.[3] Diniz, Paulo S. R. 1997, Adaptive Filtering, Algorithms and Practical Implementation. Kluwer Academic Publishers, Boston.[4] Bellanger, Maurice G., 2001. “Adaptive Digital Filters”, 2nd edition. Marcel Dekker Inc., New York.[5] Chassaing, Rulph. 2002, “DSP applications using C” John Wiley and Sons, New York.。

哈尔滨工程大学硕士学位论文摘要近场声全息技术是声场预报和声源识别的一种重要途径，通过提取声源近场附近的声场所包含的信息即可计算出声源表面声压和质点振速等声学量，进而重建出整个三维声场。

传统近场声全息技术要求所有声源均处于全息面的一边，而另一边为自由场。

实际上，声源所处的环境往往并非自由场，通常会有边界的限制，这就导致了全息测量面获得声场数据不仅仅是声源的直接辐射的声波，还包括了由于界面多次反射所产生的声波。

由此，在非自由场中，采用传统近场声全息技术通常无法实现声源的准确识别。

因此，本文提出了有限空间中基于等效源法的近场声全息技术。

本文首先针对现有的自由场中基于等效源法的近场声全息技术进行了理论研究，以点源组合和结构声源为研究对象，数值分析了该方法的可行性和有效性，并分析了全息面布放方式、全息面测点间距以及声源频率等对于重建精度的影响。

在有限空间中采用近场声全息法进行声源识别和声场重建时，由于通常会受到边界影响，无法给出格林函数的解析解。

所以本文提出采用数值计算的方式来获取有限空间中格林函数的方法，利用数值计算的格林函数来实现声源在自由场中的三维声场重建。

并将其应用于点源组合和结构声源在自由场中的声辐射预报和声场重建，分析了不同声源频率、全息面尺寸、全息测点间距以及全息面位置对于重建精度的影响。

结果表明：本文提出的方法解决了近场声全息技术只能应用于自由场和半空间声场的问题。

可以应用于非自由声场中的声场重构，具有较好的效果。

关键词：有限空间；等效源法；近场声全息技术；格林函数；声场重建ABSTRACTNear-field acoustic holography（NAH）is an important method for sound field prediction and sound source identification. Using NAH technology, the sound pressures on the surface of the sound source and the vibration velocities of the particles can be calculated by extracting sound information in the near field of the sound source, and then the entire three-dimensional sound field can be reconstructed. Traditional near-field acoustic holography technology requires all sound sources to be on the same side of the holographic surface and the other side to be a free field. Usually, the environment in which the sound source is located, however, is not a free field because of the boundary restrictions. So, the sound field data obtained by the holographic measurement surface is not only the sound waves directly radiated by the sound source, but also the multiple reflections at the interface. Therefore, the sound source cannot be identified accurately by conventional near-field acoustic holography. In this paper, proposes a near-field acoustic holography technique based on the equivalent source method in limited space has been proposed.NAH technology based on the equivalent source method in the free field is studied firstly. Then, the point source combination and structural sound source are taken as the research object, the feasibility and effectiveness of this method are analyzed numerically. And the influences of the holographic surface layout method, the distance between the measuring points of the holographic surface and the frequency of the sound source on the reconstruction accuracy have been analyzed.Aiming at the problem of sound source identification and sound field reconstruction in a limited space, the analytical solution of the Green's function cannot be given due to the limitations of the boundary properties. Therefore, this paper proposes a method to obtain the Green's function in finite space by numerical calculation，and then the three-dimensional sound field of the sound source in the free field is reconstructed by the Green’s function .It is also applied to the acoustic radiation prediction and sound field reconstruction point source combination and structured sound source. The effects of sound source frequencies, holographic surface size, holographic measurement point spacing, and holographic surface position on reconstruction accuracy are analyzed. The results show that the method proposed in this paper can be used for sound field reconstruction in non-free sound fields, and has a good effect. This method solves the limitation that traditional NAH could only be applied to free-field and half-space acoustic fields.目录第1章绪论 (1)1.1 论文背景及研究目的 (1)1.2 国内外研究现状 (2)1.2.1 近场声全息研究现状 (2)1.2.2 有限空间声场测量技术 (5)1.3 本文主要内容与章节安排 (7)1.3.1 本文主要内容 (7)1.3.2 章节安排 (7)第2章基于等效源法的近场声全息变换方法 (9)2.1 引言 (9)2.2 等效源积分方程 (9)2.3 基于等效源法的近场声全息变换方法基本原理 (11)2.4 数值仿真分析 (12)2.4.1 点源组合情况的数值仿真分析 (12)2.4.2 球壳结构近场声全息变换数值仿真分析 (14)2.5 本章小结 (18)第3章有限空间中基于等效源法的近场声全息变换方法 (21)3.1 引言 (21)3.2 有限空间中基于等效源法的近场声全息变换理论模型 (21)3.3 有限空间中声场重构 (22)3.3.1 有限元法 (22)3.3.2 有限空间中声场重构步骤 (23)3.4 有限空间中基于等效源法的近场声全息理论模型的有效性验证 (24)3.5 本章小结 (25)第4章矩形水池中近场声全息变换方法数值仿真分析 (27)4.1 引言 (27)4.2 有限空间中点源组合的数值仿真分析 (27)4.3 不同全息测量参数情况下点源组合的数值仿真分析 (31)4.3.1 全息面尺寸和测点间距对全息重建的影响 (31)哈尔滨工程大学硕士学位论文4.3.2 全息面位置对全息重建的影响 (37)4.4 本章小结 (39)第5章循环水槽中近场声全息变换方法数值仿真分析 (41)5.1 引言 (41)5.2 不同边界条件下点源组合的数值仿真分析 (41)5.2.1 阻抗边界条件 (42)5.2.2 绝对软边界 (46)5.2.3 绝对硬边界 (51)5.2.4 整体绝对硬边界 (56)5.3 球壳结构表面源强度近场声全息变换数值仿真分析 (60)5.4 本章小结 (66)结论 (68)参考文献 (70)攻读硕士学位期间发表的论文和取得的科研成果 (74)致谢 (75)第1章绪论第1章绪论1.1 论文背景及研究目的控制水下航行体的辐射噪声水平是提高其自身隐蔽性、增强自身战斗力的重要保证。

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Imagination is not to be divorced from the facts: it is a way of illuminating the facts. It works by eliciting the general principles which apply to the facts, as they exist, and then by an intellectual survey of alternative possibilities which are consistent with those principles. It enables men to construct an intellectual vision of a new world, and it preserves the zest of life by the suggestion of satisfying purposes. Youth is imaginative, and if the imagination be strengthened by discipline this energy of imagination can in great measure be preserved through life. The tragedy of the world is that those who are imaginative have but slight experience, and those who are experienced have feeble imaginations.