A three-point symmetric moving average, referred to as a weighted moving average, is of...

A three-point symmetric moving average, referred to as a weighted moving average, is of the form

(a) Determine, as a function of a and b, the frequency response of the three-point moving average in eq. (P6.47-1).

(b) Determine the scaling factor b such that has unity gain at zero frequency.

(c) In many time-series analysis problems, a common choice for the coefficient a in the weighted moving average in eq. (P6.47-1) is a = 1/2. Determine and sketch the frequency response of the resulting filter.