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1、Chapter 6Time and Frequency Characterizationof Signals and Systems,1,Chapter 61,Chapter 6 Time and Frequency Characterization,Time-Domain:,Frequency-Domain:,6.1 The Magnitude-Phase Representation ( 幅度-相位) of the Fourier Transform,Magnitude,Energy-Density,2,Chapter 6,Chapter 6 Time and Frequency Char
2、acterization,6.2 The Magnitude-Phase Representation of the Frequency Response of LTI Systems,Gain,Phase Shift,1. Linear Phase,2. Nonlinear Phase,3,Chapter 6,Chapter 6 Time and Frequency Characterization,Homework: 6.5 6.23,4,Chapter 6,6.5 Consider a continuous-time ideal bandbass filter whose frequen
3、cy response is,Chapter 6 Problem Solution,If is the impulse response of this filter, determine a 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
4、),5,6.5 Consider a continuous-tim,Chapter 6 Problem Solution,6.23 Shown in Figure 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,Chapter 6,(c),Chapter 6 Problem Solution,7,(c) C
5、hapter 6,Chapter 7 Sampling,Chapter 7 Sampling,8,Chapter 7,Chapter 7 Sampling,9,Chapter 7,Chapter 7 Sampling,Homework: 7.1 7.2 7.3 7.6 7.9,7.3 The Effect of Undersampling: Aliasing 欠采样 混叠,10,Chapter 7,Chapter 7 Problem Solution,7.1 A real-valued signal is known to be uniquely determined by its sampl
6、es when the sampling frequency is . For what values of is guaranteed to be zero?,11,Chapter 7,Chapter 7 Problem Solution,7.2 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 samplin
7、g periods would guarantee that can be recovered 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 interval,12,Chapter 7,Chapter 7 Problem Solution,7.3 Determine the Nyquist rate corresponding to each of the following signals:,13,C
8、hapter 7,Chapter 7 Problem Solution,Nyquist rate,maximum sampling interval,14,Chapter 7,Chapter 7 Problem Solution,15,Chapter 7,例 在如图1所示系统中,输入信号 的频谱如图2所示。已知 ,要求:, 画出图中信号 和 的频谱;确定T的取值范围,以使信号 能从 中恢复。,-2T -T -T1 0 T1 T 2T t,Chapter 7 Problem Solution,16,5例 在如图1所示系统中,输入信号,Chapter 8 Communication Systems
9、,17,Chapter 8 17,Chapter 8 Communication Systems,18,Chapter 8,Chapter 8 Communication Systems,Homework: 8.1 8.3 8.22,19,Chapter 8,Chapter 8 Problem Solution,20,Chapter 8,Chapter 8 Problem Solution,Solution,Be out of the passband of LPF,21,Chapter 8,8.22In Figure (a) ,a system is shown with input and
10、 outputThe input signal has the Fourier transform shown in Figure (b)Determine and sketch .,Chapter 8 Problem Solution,Figure (a),Figure (b),22,8.22 Chapter 8,-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 Solution,23,-7W -5W -3W 0 3,例 如图所示的系统中,已知输入信号 的傅
11、立叶变换 如图1所示,且 。要求:,图1, 画出图2中A、B、C各点的信号频谱; 说明这是一个做什么用的系统。,Chapter 8 Problem Solution,24,例 如图所示的系统中,已知输入信号,例 如图所示系统中,,若输入信号,,试分别A、B、C各点信号,的频谱。,Chapter 8 Problem Solution,25,ABC例 如图所示系统中,若输入信号,试分别A、B、C,Problems for Fourier Analysis,Example 4 In Figure (a), a system is shown with input signal and output
12、signal . If the following information are given.,1. Determine,2. Determine the impulse response of the whole system .,If the input signal , determine the output signal,26,Problems for Fourier AnalysisE,Problems for Fourier Analysis,27,Problems for Fourier Analysis2,Problems for Fourier Analysis,28,P
13、roblems for Fourier Analysis例,Problems for Fourier Analysis,29,Problems for Fourier Analysis,Problems for Fourier Analysis,30,Problems for Fourier AnalysisA,Problems for Fourier Analysis,If is real ,even,2. If is real ,odd,31,Example 2 A real continuous-,Problems for Fourier Analysis,1.,Solution :,32,Problems for Fourier AnalysisE,Problems for Fourier Analysis,2.,3.,33,Problems for Fourier Analysis2,