Consider down-sampling the impulse response h[n] of a filter with transfer function H(z) = 1/(1 0.5z

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Consider down-sampling the impulse response h[n] of a filter with transfer function H(z) = 1/(1 − 0.5z−1).

(a) Use MATLAB to plot h[n] and the down-sampled impulse response g[n] = h[2n].

(b) Plot the magnitude responses corresponding to h[n] and g[n] and comment on the effect of the down-sampling. Is G(e) = 0.5H(ejω/2)? Explain.

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