A three-point symmetric moving average filter, referred to as a weighted moving average is of the form
\(y[n]=b(ax[nu22121]+x[n]+ax[n+1])\)
(a) Determine as a function of a and b the frequency response
\(H(e^{j\omega})\)
of this system.
(b) Determine the scaling factor b such that
\(H(e^{j\omega})\)
has a gain of 1 when
\(\omega=0\)
(c) A common choice for a in analyzing time series is to set a=1/2. Determine and sketch the frequency response for the resulting filter.