Find the Fourier transform off (t) ={ 1, |t| < 1;0, |t| > 1.Hence evaluate the integral ∫ ∞0 sin tt dt
Question
Solution 1
The Fourier transform of a function f(t) is given by the integral:
F(ω) = ∫ f(t) e^(-iωt) dt, from -∞ to ∞
For the given function f(t) = 1 for |t| < 1 and 0 for |t| > 1, the Fourier transform becomes:
F(ω) = ∫ e^(-iωt) dt, from -1 to 1
This integral can be solved by breaking it into real and ima Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.
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