Problem 3

Fourier series analysis of moving average filter with periodic input. Revisit Problem 4,

Homework 3. Consider a moving average filter with the following impulse response A (the impulse

response is zero outside of the displayed time interval):

The input to this filter is the following periodio cignal se (T-

T

The dashed line shows one isolated period.

Answer the following,

1. Determine the Fourier series for the periodic inputs. In particular, derive an expression for

the Fourier series coefficients.

2. Determine the frequency response of the moving average filter. Hint: compute the Fourier

transform of the impulse response.

3. Determine the Fourier series coefficients for the periodic output p

4. Use Matlab to compute a partial sum of the Fourier series for y with

-1000,-900,1,0,1,999, 1000

on the time grid t = [-3:0.001:3]. Compare this result to the graphical convolution ap-

proach from Homework 3.