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1、Chapter 6Time and Frequency Characterizationof Signals and Systems1 Chapter 6 Time and Frequency CharacterizationTime-Domain:Frequency-Domain:6.1 The Magnitude-Phase Representation （ 幅度幅度-相位）相位） of the Fourier TransformMagnitude Energy-Density2 Chapter 6 Time and Frequency Characterization6.2 The Ma
2、gnitude-Phase Representation of the Frequency Response of LTI SystemsGain Phase Shift1. Linear Phase2. Nonlinear Phase3 Chapter 6 Time and Frequency CharacterizationHomework: 6.5 6.2346.5 Consider a continuous-time ideal bandbass filter whose frequency response is Chapter 6 Problem Solution(a)If is
3、the impulse response of this filter, determine a (b)function such that (b) As is increased, does the impulse response of the filterget more concentrated or less concentrated about the origin?Solution (b) It will get more concentrated about the origin.(a)5 Chapter 6 Problem Solution6.23 Shown in Figu
4、re 6.23 is for a lowpass filter. Determine and sketch the impulse response of the filter for each of the following phase characteristics: (a) (b) , where T is a constant.6(c) Chapter 6 Problem Solution7 Chapter 7 Sampling Chapter 7 Sampling8 Chapter 7 SamplingSampling Theorem:Let be a band-limited s
5、ignal withThen is uniquely determined by its samples if where9 Chapter 7 SamplingHomework: 7.1 7.2 7.3 7.6 7.97.3 The Effect of Undersampling: Aliasing 欠采样欠采样 混叠混叠10 Chapter 7 Problem Solution7.1 A real-valued signal is known to be uniquely determined by its samples when the sampling frequency is .
6、For what values of is guaranteed to be zero?11 Chapter 7 Problem Solution7.2 A continuous-time signal is obtained at the output of an ideal lowpass filter with cutoff frequency . If impulse-train sampling is performed on ,which of the following sampling periods would guarantee that can be recovered
7、from its sampled version using an appropriate lowpass filter? (a) T=0.510-3 (b) T=210-3 (c) T=10-4(a) and (c)Sampling interval12 Chapter 7 Problem Solution7.3 Determine the Nyquist rate corresponding to each of the following signals:13 Chapter 7 Problem Solution7.6 Determine the maximum sampling int
8、erval T such that is recoverable from through the use of an ideal LPF.Nyquist ratemaximum sampling interval14 Chapter 7 Problem Solution7.9 Consider the signalwhich we wish to sample with a sampling frequency ofto obtain a signal with Fourier transform . Determinethe maximum value of for which it is
9、 guaranteed that155例例 在如图在如图1所示系统中所示系统中,输入信号输入信号 的频谱如图的频谱如图2所示。所示。已知已知 ，要求：，要求： 画出图中信号画出图中信号 和和 的频谱；的频谱；确定确定T的取值范围，以使信号的取值范围，以使信号 能从能从 中恢复。中恢复。-2T -T -T1 0 T1 T 2T t Chapter 7 Problem Solution16 Chapter 8 Communication Systems17 Chapter 8 Communication SystemsModulation :The general process of embed
10、ding an information-bearing signal into a second signal.Extracting the information-bearing signal.Demodulation :Modulation :Amplitude Modulation (AM)Frequency Modulation (FM)Phase Modulation (PM)18 Chapter 8 Communication SystemsHomework: 8.1 8.3 8.2219 Chapter 8 Problem Solution8.1 Determine a sign
11、al such that Solution 20 Chapter 8 Problem Solution8.3 Determine . LPF Solution Be out of the passband of LPF21 8.22In Figure (a) ,a system is shown with input and outputThe input signal has the Fourier transform shown in Figure (b)Determine and sketch . Chapter 8 Problem SolutionFigure (a)Figure (b
12、)22-7W -5W -3W 0 3W 5W 7W -5W -3W 0 3W 5W -8W -6W -2W 0 2W 6W 8W -2W 0 2W Chapter 8 Problem Solution23例例 如图所示的系统中，已知输入信号如图所示的系统中，已知输入信号 的傅立叶变换的傅立叶变换 如图如图1所示，且所示，且 。要求：。要求：ABC1图图1 画出图画出图2中中A、B、C各点的信号频谱；各点的信号频谱； 说明这是一个做什么用的系统。说明这是一个做什么用的系统。 Chapter 8 Problem Solution24ABC例例 如图所示系统中，如图所示系统中，若输入信号若输入信号，
13、试分别，试分别A、B、C各点信号各点信号的频谱。的频谱。 Chapter 8 Problem Solution25Problems for Fourier AnalysisExample 4 In Figure (a), a system is shown with input signal and output signal . If the following information are given.1. Determine 2. Determine the impulse response of the whole system .3.If the input signal , 4.
14、determine the output signal +-26Problems for Fourier Analysis27Problems for Fourier Analysis例例 如图所示系统中，已知如图所示系统中，已知 ，且且 ，概略画出，概略画出 ， ， 和和的的波形。说明整个系统等价于一个带通滤波器，波形。说明整个系统等价于一个带通滤波器，并并用用 和和 确定带通滤波器的上、下截止频率确定带通滤波器的上、下截止频率28Problems for Fourier Analysis Consider an LTI system with unit impulse response 2
15、. If the input is determine the output 1. Determine the frequency response of the whole system. 29Problems for Fourier AnalysisA period of Example 1 Determine the Fourier transform of30Example 2 A real continuous-time signal with Fourier transform , and 1.If is even, determine .2.If is odd, determine .Problems for Fourier Analysis1.If is real ,even2. If is real ,odd31Problems for Fourier AnalysisExample 3 Consider the following LTI systems with impulse response:1. 2.3.If the input is Determine the output 1. Solution :32Problems for Fourier Analysis2.3.33
