(Solved): The discrete moving average filter is characterised by the following Difference Equation: \[ y[n]= ...

The discrete moving average filter is characterised by the following Difference Equation: \[ y[n]=\frac{1}{3}(x[n+1]+x[n]+x[n-1]) \] a) Find the Frequency Response of this filter and express it in the form of \( a+b \cos \omega \), where \( a \) and \( b \) are both constants to be determined. b) Conclude the periodic Magnitude and Phase spectra of the filter and plot them for \( 0 \leq \omega \leq \pi \). c) The discrete periodic signal \( e^{j \pi n} \) is applied to the input of the given filter. Find the time-domain response of the system and express it in terms of the discrete time variable \( n \). d) Comment on the stability of the filter and justify your answer.