An ideal C/D converter is followed by a discrete-time LPF which is followed by an ideal D/C converter. The sampling rate is 8000 samples per second. The input analog signal is bandlimited to 3900 Hz. The overall frequency response is required to satisfy the following: Gain > -1.33 dB for frequencies less than 1, 333.33 Hz Gain < -7.5 dB for frequencies greater than 2, 133.33 Hz
a) Generate specifications on the discrete-time filter and design the LPF using the BLT and the Butterworth design technique.
b) Obtain the transfer functions of both the analog and the discrete-time filters.
c) Verify, by obtaining it from the transfer function and plotting it, that the frequency response of the designed discrete-time filter satisfies the specifications.
d) Give reason(s) as to why one cannot simply use the direct mapping from analog to digital frequency as given by the sampling theorem but the frequency warping relationships of the BLT have to be used instead.