Question

What is the form of the FIR system to compute the moving average of the signal x(n)?

(a) y(n)=\(\frac{1}{M+1} \sum_{k=0}^M x(n-k)\)

(b) y(n)=\(\frac{1}{M+1} \sum_{k=0}^M x(n+k)\)

(c) y(n)=\(\frac{1}{M+1} \sum_{k=0}^{\infty} x(n-k)\)

(d) None of the mentioned

I got this question by my college professor while I was bunking the class.

This interesting question is from Implementation of Discrete Time Systems topic in portion Discrete Time Signals and Systems of Digital Signal Processing

Answer 1

The correct answer is (a) y(n)=\(\frac{1}{M+1} \sum_{k=0}^M x(n-k)\)

For explanation: A normal FIR non-recursive system with the impulse response h(n)=\(\frac{1}{M+1}\) is the system which is used to compute the moving average of a signal x(n).