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Show all your work for each problem. 1. Given the following DSP system with a sampling rate 8000 Hz, y(0.5x(n)-0.5x(n -1) where y(n) is the output and x(n) is the input a) Find its transfer function, b) Make a pole-zero plot and determine the stability. c) Obtain He) and then He) d) Compute the filter gain at the frequency of 0 Hz, 1000 Hz, 2000 Hz, 3000Hz, 4000 Hz, respectively e Make a magnitude frequency response plot. f) Determine the filter typ e, that is, the lowpass filter, or high pass filter, or bandpass filter, or bandstop filter.

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