Question

What is the magnitude of H(ω) for the three point moving average system whose output is given by y(n)=\(\frac{1}{3}[x(n+1)+x(n)+x(n-1)]\)?

(a) \(\frac{1}{3}|1-2cosω|\)

(b) \(\frac{1}{3}|1+2cosω|\)

(c) |1-2cosω|

(d) |1+2cosω|

I have been asked this question in examination.

I would like to ask this question from Frequency Domain Characteristics of LTI System topic in section Frequency Analysis of Signals and Systems of Digital Signal Processing

Answer 1

Right option is (b) \(\frac{1}{3}|1+2cosω|\)

Easiest explanation: For a three point moving average system, we can define the output of the system as

y(n)=\(\frac{1}{3}[x(n+1)+x(n)+x(n-1)]=>h(n)=\{\frac{1}{3}, \frac{1}{3}, \frac{1}{3}\}\)

it follows that H(ω)=\(\frac{1}{3}(e^{jω}+1+e^{-jω})=\frac{1}{3}(1+2cosω)\)

=>| H(ω)|=\(\frac{1}{3}\)|1+2cosω|