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Question 6.10: Step Response of a First-Order Digital Lowpass Filter Comput...

Step Response of a First-Order Digital Lowpass Filter
Compute and plot the input and output samples for n = 0 to 20, given a = 0.9. The input is a step function defined by

x(n) = 0 for n < 0

= 1 for n ≥ 0

Assume that y(n) = 0 for n < 0.

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We have

y(0)=ay(-1)+(1-a)x(0)=0.9\times 0+0.1\times 1=0.1

y(1)=ay(0)+(1-a)x(1)=0.19

y(2)=ay(1)+(1-a)x(2)=0.71

…

y(22)=0.8906

Plots of x(n) and y(n) are shown in Figure 6.49. Notice that the response of the digital filter to a step input is very similar to that of the RC filter shown in Figure 4.4 on page 171

6.49
Screenshot 2022-12-19 221111

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