If F() is the Fourier transform of f(x), show that the inverse Fourier transform of

Chapter 10, Problem 10.3.5

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QUESTION:

If F() is the Fourier transform of f(x), show that the inverse Fourier transform of eiF() is f(x ). This result is known as the shift theorem for Fourier transforms.

Questions & Answers

QUESTION:

If F() is the Fourier transform of f(x), show that the inverse Fourier transform of eiF() is f(x ). This result is known as the shift theorem for Fourier transforms.

ANSWER:

Step 1 of 3

Let   be the Fourier transform of the function  .

The objective is to show that the inverse Fourier transform of   is

Since   is the Fourier transform of the function  ,

So, the inverse Fourier transformation of the function   is,

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