2.35. Show that the Fourier transform of x(t)= e-*² is X(f) = e-f². This is an example of a signal whose Fourier transform is of the same functional form as the signal itself. [Hint: Complete the square in the exponent of the Fourier transform integral and use Se-au du = √√/a.]

2.35. Show that the Fourier transform of x(t)= e-*² is X(f) = e-f². This is an example of a signal whose Fourier transform is of the same functional form as the signal itself. [Hint: Complete the square in the exponent of the Fourier transform integral and use Se-au du = √√/a.]

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

2.35. Show that the Fourier transform of x(t) = e-²
is X(f) = e-f². This is an example of a signal whose
Fourier transform is of the same functional form as
the signal itself. [Hint: Complete the square in the
exponent of the Fourier transform integral and use
Se-au² du = √/α.]

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Step 1: Determine Fourier transform for given signal x(t):

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Step 2: Define Fourier transform to find X(w):

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Step 3: Find X(f):

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Step 4: Use FT properties to find X(f) (METHOD II) :

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Step 5: Find FT in time domain:

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Step 6: Find X(f) in frequency domain:

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