FIR and IIR filters: symmetry of impulse response and linear-phase Consider two FIR filters with transfer functions
Question:
FIR and IIR filters: symmetry of impulse response and linear-phase— Consider two FIR filters with transfer functions
H1(z) = 0.5 + 0.5z−1 + 2.2z−2 + 0.5z−3 + 0.5z−4
H2(z) = − 0.5 − 0.5z−1 + 0.5z−3 + 0.5z−4
(a) Find the impulse responses h1[n] and h2[n] corresponding to H1(z) and H2(z). Plot them carefully and determine the sample with respect to which these impulse responses are even or odd.
(b) Show frequency response for G(z) = z2 H1 (z) is zero-phase, and from it determine the phase of H1(ejω). Use MATLAB to find the unwrapped phase of H1(ejω) and confirm your analytic results.
(c) Find the phase of H2(ejω) by finding the phase of the frequency response for F(z) = z2 H2 (z). Use MATLAB to find the unwrapped phase of H2(ejω). Is it linear?
(d) If H(z) were the transfer function of an IIR filter, according to the above arguments could it be possible for it to have linear phase? Explain.
Step by Step Answer:
a The impulse responses are h 1 n is even with respect to the sample at n 2 while h 2 n is odd with ...View the full answer
