Find the Fourier transform of f (t) = 1- |t| if |t|< 1; 0 if |t| > 1 and prove ∫[from 0 to ∞] (sint/t)^4 dt= pi/3

Question

Find the Fourier transform of f (t) = 1- |t| if |t|< 1; 0 if |t| > 1 and prove ∫[from 0 to ∞] (sint/t)^4 dt= pi/3
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Solution 1

Sure, let's break this down into two parts.

Part 1: Fourier Transform of f(t)

The function f(t) is defined as:

f(t) = 1 - |t| for |t| < 1 = 0 for |t| > 1

The Fourier Transform of f(t) is given by:

F(ω) = ∫[from -∞ to ∞] f(t) e^(-iωt) dt

We can split this integral into two parts, from -1 Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

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Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
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