英文版《信号与系统》第六七八章习题解答.ppt

Homework:6.5 6.23 6.27Chapter 6 Problem Solution7.1 7.2 7.3 7.6 7.98.1 8.3 8.22 8.286.5 Consider a continuous-time ideal bandbass filter whose frequency response is Chapter 6 Problem Solution(a) If is the impulse response of this filter, determine a function such that (b) As is increased, does the impulse response of the filter get more concentrated or less concentrated about the origin?Solution (b) It will get more concentrated about the origin.(a)Chapter 6 Problem Solution6.23 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.(c)Chapter 6 Problem SolutionChapter 6 Problem Solution6.27 The output of a causal LTI system is related to the input by the differential equation(a) Determine the frequency response of the system, and sketch its Bode plot.(b) Specify, as a function of frequency, the group delay associated with this system.Chapter 6 Problem Solutiongroup delay (c) If , determine , the Fourier transform ofthe output.(d) Using the technique of partial-fraction expansion,determine the output for the input in part (c).(e) Repeat parts (c) and (d), first if the input has as itsFourier transformChapter 6 Problem SolutionChapter 7 Problem Solution7.1 A real-valued signal is known to be uniquely determinedby its samples when the sampling frequency is . For what values of is guaranteed to be zero?Chapter 7 Problem Solution7.2 A continuous-time signal is obtained at the output of an ideallowpass filter with cutoff frequency . If impulse-trainsampling is performed on ,which of the following samplingperiods would guarantee that can be recovered from itssampled version using an appropriate lowpass filter?(a) T=0.5×10-3(b) T=2×10-3(c) T=10-4(a) and (c)Sampling intervalChapter 7 Problem Solution7.3 Determine the Nyquist rate corresponding to each of the following signals:Chapter 7 Problem Solution7.6 Determine the maximum sampling interval T such that is recoverable from through the use of an ideal LPF.Nyquist ratemaximum sampling intervalChapter 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 guaranteed thatChapter 8 Problem Solution8.1 Determine a signal such that Solution Chapter 8 Problem Solution8.3 Determine . LPF Solution Be out of the passband of LPF8.22In 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)-7W -5W -3W 0 3W 5W 7W ω-5W -3W 0 3W 5W ω-8W -6W -2W 0 2W 6W 8W ω-2W 0 2W ωChapter 8 Problem SolutionChapter 8 Problem SolutionSolution:8.28 SSB system using a 90o phase-shift network required toretain the upper sideband.90o phase-shiftChapter 8 Problem SolutionUpper SidebandProblems for Fourier AnalysisA period of Example 1Determine the Fourier transform ofExample 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 ,evenProblems for Fourier Analysis2. If is real ,oddProblems for 。