Frequency Response of FIR Filters

Filtering Sampled Continuous-Time Signalsyn =He jˆXe jˆ n(6.37)• We can write yn in terms of the analog frequency variable via ˆ = T syn =He jT s Xe jT sn(6.38)• At the output of the D-to-C converter we have the reconstructedoutputyt ==He jT s Xe jtHe j2f f sXe j 2f f st(6.39)where f is the input analog sinusoid frequency (perhaps a betternotation would be f 0 0ˆ 0 )Example: Lowpass Averager• Consider a 5-point moving average filter wrapped upbetween a C-to-D and D-to-C system• We assume a sampling rate of 1000 Hz and an input composedof two sinusoidsxt =cos2100t+3cos2300t• Find the system frequency response in terms of the analogfrequency variable f, and find the steady-state output yt • We will use freqz() to obtain the frequency response>> w = -pi:pi/100:pi;>> H = freqz(ones(1,5)/5,1,w);>> subplot(211)ECE 2610 Signals and Systems 6–28