What is the Fourier transform of the following functions, and how fast do they decay? a) f(t) = {e-t, t>=0; 0, t<0} b)f(t) = {e-|t|, t>=0; 0, t<0}
What is the Fourier transform of the following functions, and how fast do they decay? a) f(t) = {e-t, t>=0; 0, t<0} b)f(t) = {e-|t|, t>=0; 0, t<0}
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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Question
What is the Fourier transform of the following functions, and how fast do they decay?
a) f(t) = {e-t, t>=0; 0, t<0}
b)f(t) = {e-|t|, t>=0; 0, t<0}
Expert Solution
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The Fourier transform is a mathematical operation that separates the frequencies that make up a waveform, which is a function of time. Fourier transform is a mathematical transformation that breaks down functions that rely on either time or space into functions that depend on either time or spatial frequency. Another name for the procedure is analysis. The Fourier transform's output is a complex-valued function of frequency.
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