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

What is the magnitude of H(ω) for the three point moving average syst

1.	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» 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\|

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