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Mathematics
Calculus
Peak of Analytical Fourier Transform
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[QUOTE="Luke Tan, post: 6314943, member: 645630"] [B]TL;DR Summary:[/B] Finding the peak frequency in an analytical fourier transform In a numerical Fourier transform, we find the frequency that maximizes the value of the Fourier transform. However, let us consider an analytical Fourier transform, of ##\sin\Omega t##. It's Fourier transform is given by $$-i\pi\delta(\Omega-\omega)+i\pi\delta(\omega+\Omega)$$ Normally, to find the value of ##\omega## that maximizes this function, we would differentiate with respect to ##\omega## and set to 0. However, in this case, the derivative of a dirac delta function cannot be evaluated. Hence, we are unable to find the peak frequency to be at ##\Omega## unlike what we would in a numerical, discrete-time Fourier transform. Is there any way around this, to find the peak frequency of the Fourier transform of a function? [/QUOTE]
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Mathematics
Calculus
Peak of Analytical Fourier Transform
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