An FIR filter has a transfer function H(z) = z 2 (ze jÏ/2 )(ze jÏ/2 ). (a) Find and plot the poles and zeros of

An FIR filter has a transfer function H(z) = z^ˆ’2(zˆ’e^jÏ€/2)(zˆ’e^{ˆ’jÏ€/2}).

(a) Find and plot the poles and zeros of this filter.

(b) Expressing the frequency response at some frequency ω₀ as   

carefully draw the vectors on the pole-zero plot.

(c) Consider the case when ω₀ = 0, find H(e^j0) analytically and  using the vectors.

(d) Repeat the above calculations for ω₀ = Ï€ and ω₀ = ± Ï€/2 (verify  your result from the given Z-transform). Can you classify this filter?

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