Homework: 6.5 6.23 6.27,7.1 7.2 7.3 7.6 7.9,8.1 8.3 8.22 8.28,6.5 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 filterget more concentrated or less concentrated about the origin?,Solution,(b) It will get more concentrated about the origin.,(a),(b) , where T is a constant.,(c),(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.,(d) Using the technique of partial-fraction expansion,determinethe output for the input in part (c).,(e) Repeat parts (c) and (d), first if the input has as its Fourier transform,7.1 A real-valued signal is known to be uniquely determined by its samples when the sampling frequency is . For what values of is guaranteed to be zero?,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 appropriate lowpass filter? (a) T=0.510-3 (b) T=210-3 (c) T=10-4,(a) and (c),Sampling interval,7.3 Determine the Nyquist rate corresponding to each of the following signals:,Nyquist rate,maximum sampling interval,Solution,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 .,Figure (a),Figure (b),Solution:,If is real ,even,2. If is real ,odd,Solution :,2.,3.,(b) If , there is no overlap.,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,1. Determine,If the i