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Filtering Sampled Continuous-Time SignalsInterpretation <strong>of</strong> Delay• In the study <strong>of</strong> the moving average filter, it was noted thatwhereD Le jˆHe jˆ• The pure delay systemhas impulse responseand has frequency response D Le jˆ –e jˆ L – 1=is a purely real functionyn = xn – n 0hn = n–n 0– e jn 0ˆ=He jˆ• We also know that the impulse response <strong>of</strong> two systems incascade ishn He jˆh 1n*h 2n• The L-point moving average filter thus incorporates a delay<strong>of</strong> L – 1 2 samples• Viewed as a cascade <strong>of</strong> subsystemsHe jˆ– If L is odd then the delay is an integer= = H 1e jˆ 2H 2e jˆ D Le jˆ – e jˆ L – 1= – If L is even then the delay is an odd half integer(6.45)ECE 2610 Signals and Systems 6–32 2
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