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If H(z) is the z-transform of the impulse response of an FIR filter, then which of the following relation is true?(a) z^M+1.H(z^-1)=±H(z)(b) z^-(M+1).H(z^-1)=±H(z)(c) z^(M-1).H(z^-1)=±H(z)(d) z^-(M-1).H(z^-1)=±H(z)I have been asked this question in an interview for internship.Asked question is from Design of FIR Filters in division Digital Filters Design of Digital Signal Processing

Answer»

The correct choice is (d) z^-(M-1).H(z^-1)=±H(z)

Easy explanation: We know that H(z)=\(\sum_{K=0}^{M-1} h(k)z^{-k}\) and h(N)=±h(M-1-n) n=0,1,2…M-1

When we incorporate the symmetric and anti-symmetric conditions of the second equation into the first equation and by substituting z^-1 for z, and multiply both SIDES of the resulting equation by z^-(M-1) we get z^-(M-1).H(z^-1)=±H(z)



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