Find the exponential Fourier Transform of the given function and write the function as a Fourier Integral, that is use Equation 7.12.2 to find g(a) and substitute this into the first integral in Equation 7.12.2. -1 - T (4.1)

Find the exponential Fourier Transform of the given function and write the function as a Fourier Integral, that is use Equation 7.12.2 to find g(a) and substitute this into the first integral in Equation 7.12.2. -1 - T (4.1)

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter4: Calculating The Derivative

Section4.CR: Chapter 4 Review

Problem 5CR: Determine whether each of the following statements is true or false, and explain why. The chain rule...

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Question

Find the exponential Fourier Transform of the given function and write the function as
a Fourier Integral, that is use Equation 7.12.2 to find g(x) and substitute this into the
first integral in Equation 7.12.2.
f(x) = {₁¹
-1 -π<x<0
0<x<T
; f(x) = 0 when |x| > T
(4.1)

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Step 1: Write the definition of the exponential Fourier transform

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Step 2: Use the definition

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Step 3: Determine the required Fourier transform

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