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Question 6.11: 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)=0.271 \\ … \\ y(20)=0.8906

Plots of x(n) and y(n) are shown in Figure 6.48. 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 192. 

6.48
4.4

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