Use Eigenfunctions to solve Suppose we have a system with the following transfer function.H(s) = s + 2Find the output if the input is:x(t) = cos(2t)

Answered: Suppose we have a system with the…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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Use Eigenfunctions to solve

Suppose we have a system with the following transfer function.
H(s) = s + 2
Find the output if the input is:
x(t) = cos(2t)

Expert Solution

Step 1: Write the formula to be used

To solve this problem using eigenfunctions, we can utilize the concept of eigenfunctions of linear time-invariant systems, particularly when dealing with linear differential equations. The eigenfunctions of a system are functions that remain unchanged (apart from scaling) when passed through the system. In this case, we'll find the eigenfunctions of the given system characterized by the transfer function $H (s) = s + 2$ .

The general form of an eigenfunction solution for a linear time-invariant system with transfer function $H (s)$ and input $x (t)$ is given by:

$integral subscript negative infinity end subscript superscript infinity$

Here, $H (t - τ)$ is the impulse response of the system, and $x (τ)$ is the input signal.

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