(a) An ideal lowpass filter with impulse response h[n] is designed with zero phase,...

(a) An ideal lowpass filter with impulse response h[n] is designed with zero phase, a cutoff frequency of ω_c = π/4, a passband gain of 1, and a stopband gain of 0. (H(e^jω) is shown in Figure P5.21.) Sketch the discrete-time Fourier transform of (−1)ⁿh[n].

(b) A complex-valued filter with impulse response g[n] has the pole–zero diagram shown in Figure P5.25. Sketch the pole–zero diagram for (−1)ⁿg[n]. If there is not sufficient information provided, explain why.