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TEXT 3.2 Digital Signal Processing
1. Introduction 2. Fourier Analysis 3. FIR digital filter design 4. Window Functions
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Terminology
• fidelity n.保真度, (收音机, 录音设备等的) 逼真度, 保真度, 重现精度 • sensory adj.感觉的, 感官的 • seismic adj.[地]地震的 • vibrations n.振动, 颤动, 摇动, 摆动 • storage n.贮藏(量), 贮藏库, 存储 • superposition n.重叠, 重合, 叠合 • ubiquitous adj.到处存在的, (同时)普遍存在的 • utility n.效用, 有用
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• At present, many digital signal processing methods have been widely used in science and technology fields. So we take digital signal system for example, some system properties are described in next section.
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A continuous-time system is a system in which continuous-time input signals are applied and result in continuous-time output signals. As in Figure 3-1-5(a), where x(t) is the input, y(t) is the output, and h(t) is the system impulse response.
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• • • • • • • • • • •
physical adj. 自然的, 物理的 delay v.耽搁, 延迟, 延期, 迟滞 re-indexing 改变符号 oscillatory adj.摆动的 ripple n.波纹 transition n.转变, 转换, 跃迁, 过渡, 变调 Gibbs phenomenon. Gibbs现象 sub-optimum adj.未达最佳标准的 mainlobe n.主瓣 sidelobe n.旁瓣 attenuation n.衰减
T { x(n − n0 )} = y (n − n0 )
Linearity and time invariance are independent properties.
) ∗ y (n) = y (n) ∗ x (n)
Associative:
x ( n ) * y ( n ) * w ( n ) = x ( n ) * y ( n ) * w ( n )
②signals ③signals ①Signals
is those with finite average power
.
P∞
is the signals for which neither P nor ∞
E∞
are finite.
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EXERCISES
• 1. Please translate the following words and phrases into Chinese. • 2. Please translate the following words and phrases into English.
Chapter 3 Signal System & Signal Processing
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• 3.1 Signal and System • 3.2 Digital Signal Processing • 3.3 Speech Signal Processing
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TEXT 3.1 Signal and System
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• transformed by the system or cause the system to respond in some way, resulting in other signals as outputs. For example, a high-fidelity system takes a recorded audio signal and generates a reproduction of that signal. If the hifi system has tone controls, we can change the t on a l qu a lit y o f th e re p ro d u c e d sig n a l
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• 1. Continuous-time and discrete-time signals • 2. Continuous-time and discrete-time systems • 3. Some properties of digital signal system • 4. Signal energy and power
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• eg.2 a picture can be represented by brightness as a function of two spatial variables
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(⋅)
• To distinguish between continuous-time and discrete-time signals, we will use the symbol t to denote the continuous-time independent variable which is enclosed in parentheses (.) and n to denote the discrete-time independent variable in brackets [.].
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• Illustrations of a continuous-time signal and a discrete-time signal are shown in Fig.3-4.
• •
•
(a)
(b)
Fig. 3-4 Graphical representations of (a) continuous-time and (b) discrete-time signals
• Simply introduction of the mathematical representations of continuous-time and discrete-time signals and systems, and the concepts of signal energy and power.
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Terminology
• • • • • • • • • • • • aeronautics n.航空学, 航空术 astronautics n.太空航空学 seismology n.地震学 meteorologic adj.气象的, 气象学的 profile n.剖面, 侧面, 外形, 轮廓 convention n.大会, 协定, 习俗, 惯例 terminology n.术语学 electromechanical adj.[机]电动机械的,机电的,电机的 automotive adj.汽车的, 自动推进的 vehicle n.交通工具, 车辆 high-fidelity 高保真 tone n.音调, 音质, 语调
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2. Continuous-time and discrete-time systems
• Physical systems in the broadest sense are an interconnection of components, devices, or subsystems. In context ranging from signal processing and communications to electromechanical motors, automotive vehicles, and chemical-processing plants, a system can be viewed as a process in which input signals are
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1.Continuous-time and discrete-time signals • Signals are represented mathematically as functions of one or more independent variables: eg.1: a speech signal can be represented mathematically by acoustic pressure as a function of time
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• We can bring continuous-time and discrete-time systems together through the concept of sampling, and we can develop some insights into the use of discrete-time systems to process continuous-time signals that have been sampled.
Distributive:
x ( n ) * y ( n ) + w ( n ) = x ( n ) * y ( n ) + x ( n ) * w ( n )
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4. Signal energy and power