1、1,Homework: 6.5 6.23,7.1 7.2 7.3 7.6 7.9,8.1 8.3 8.22 8.28,2,6.5 Consider a continuous-time ideal bandbass filter whose frequency response is,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 o

2、r less concentrated about the origin?,Solution,(b) It will get more concentrated about the origin.,(a),3,(b) , where T is a constant.,4,(c),5,6,(b) Specify, as a function of frequency, the group delay associated with this system.,group delay,(c) If , determine , the Fourier transform of the output.,

3、(d) Using the technique of partial-fraction expansion,determine the output for the input in part (c).,7,(e) Repeat parts (c) and (d), first if the input has as its Fourier transform,8,7.1 A real-valued signal is known to be uniquely determined by its samples when the sampling frequency is . For what

4、 values of is guaranteed to be zero?,9,7.2 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 sampling periods would guarantee that can be recovered from its sampled version using an

5、appropriate lowpass filter? (a) T=0.510-3 (b) T=210-3 (c) T=10-4,(a) and (c),Sampling interval,10,7.3 Determine the Nyquist rate corresponding to each of the following signals:,11,Nyquist rate,maximum sampling interval,12,13,14,Solution,15,8.22 In Figure (a) ,a system is shown with input and output

6、The input signal has the Fourier transform shown in Figure (b) Determine and sketch .,Figure (a),Figure (b),16,17,Solution:,18,19,20,If is real ,even,21,2. If is real ,odd,22,Solution :,23,2.,3.,24,25,(b) If , there is no overlap.,26,Example 5 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 .,If the input signal , determine the output signal,27,1. Determine,28,29,If the input signal ,