Question
Determine the Fourier transform of the function :
Answer :
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The Fourier transform of the given function can be determined as follows: Given the function: [ f(t) = \begin{cases} \sin(3t) & \text{for } -\pi \le t \le \pi, \ 0 & \text{otherwise}. \end{cases} ] The Fourier transform ( F(\omega) ) is defined as: [ F(\omega) = \int_{-\infty}^{\infty} f(t) e^{-i\omega t} , dt ] Since ( f(t) = 0 ) outside the interval ( -\pi \le t \le \pi
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