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Problem 6. (C05) Show that the convolution z of the following two signals #(t) = e-a!4| =e-ble|

Problem 6. (C05) Show that the convolution z of the following two signals #(t) = e-a!4| =e-ble|

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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Problem 6. (C05) Show that the convolution z of the following two signals ¤(t) = e-ale| (6a) y(t) = e-ble| (6b)
Transcribed Image Text:Problem 6. (C05) Show that the convolution z of the following two signals ¤(t) = e-ale| (6a) y(t) = e-ble| (6b)
where a, b > 0 and a + b + 0, is given by (6c) 26 2a -히티 a #b + z(t) (비 + 공) e-c비 (6d) a = b = c> 0 Hint: Use the fact that any signal of the form e-alel can be written as eatu(-t) +e-atu(t) (verify this!) and then use convolution properties to minimize the amount of convolutions you need to calculate.
Transcribed Image Text:where a, b > 0 and a + b + 0, is given by (6c) 26 2a -히티 a #b + z(t) (비 + 공) e-c비 (6d) a = b = c> 0 Hint: Use the fact that any signal of the form e-alel can be written as eatu(-t) +e-atu(t) (verify this!) and then use convolution properties to minimize the amount of convolutions you need to calculate.
Expert Solution
Step 1

We are given two functions:

xt=e-at;yt=e-bt

We have to find convolution of x(t) and y(t) for two cases:

  • when a≠b.
  • when a=b=c>0.
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