Question

Which of the following filters have a cascade realization as shown below?

(a) IIR filter

(b) Comb filter

(c) High pass filter

(d) FIR filter

This question was addressed to me by my college professor while I was bunking the class.

My doubt stems from Structures for FIR Systems topic in portion Discrete Time Systems Implementation of Digital Signal Processing

Answer 1

The correct choice is (d) FIR filter

To explain: The system function of the FIR filter according to the frequency sampling realization is given by the equation

H(z)=\(\frac{1}{M}(1-z^{-M} e^{j2πα})\sum_{k=0}^{M-1}\frac{H(k+α)}{1-e^{\frac{j2π(k+α)}{M}} z^{-1}}\)

The above system function can be represented in the cascade form as shown in the above block diagram.