Find the Fourier transform off (t) ={ 1 − |t|, if |t| < 1;0, |t| > 1and hence deduce that∫ ∞0( sin tt)4dt = π3
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 - |t| for |t| < 1 and 0 for |t| > 1, the Fourier transform becomes:
F(ω) = ∫ (1 - |t|) e^(-iωt) dt, from -1 to 1
This integral can be split into two parts, o Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.
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Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.
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