An analog signal x(t) consists of the sum of two components x1(t) and x2(t). The spectral characteristics of x(t) are shown in figure. The signal x(t) is bandlimited to 40 kHz and it is sampled at a rate of 100 kHz to yield the sequence x(n).
(b) Compare the order M obtained in part (a) with the approximate formulas given in equations (8.2.94) and (8.2.95).
(c) For the order M obtained in part (a), design an FIR digital lowpass filter using the window technique and the Hamming window. Compare the frequency response characteristics of this design with those obtained in part (a).
(d) Design the minimum-order elliptic filter that meets the given amplitude specifications. Compare the frequency response of the elliptic with that of the FIR filter in part (a).
(e) Compare the complex of implementing the FIR filter in part (a) versus the elliptic filter obtained in part (d). Assume that the FIR filter is implemented in the direct form and the elliptic filter is implemented as a cascade of two-pole filters. Use storage requirements and the number of multiplications per output point in the comparison ofcomplexity.
This question was answered on: Jul 11, 2017
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