Fourier Transforms Calculator

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Example

Created on 2024-06-20Asked by Theodore Rodriguez (Solvelet student)

Find the Fourier transform of the function

f(x) = e^{-|x|}

Solution

To find the Fourier transform of the function

f(x) = e^{-|x|}

\mathcal{F}[f(x)] = \sqrt{\frac{2}{\pi}} \frac{1}{1 + \omega^2}.

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Some of the related questions asked by Noah Thompson on Solvelet

1. Compute the Fourier transform of the function

f(x) = e^{-}

.2. Find the Fourier transform of the function

g(x) = e^{-x}

DefinitionDefine: Fourier transforms are mathematical techniques to represent functions in terms of their frequency values. They transform the function from the time or spatial domain to the frequency domain showing the frequency content, the amplitude of the function, and the phase shift for a sine wave of that frequency. Transform=frequency component of time/period. Fourier transforms decompose signals into a set of complex exponentials, which are a subset of sinusoids. They are instrumental in signal processing, communication systems, and scientific analysis. The Fourier transform is known as an integral transform. The Fourier transform and its inverse transform a function from the frequency domain back to the time or spatial domain. Example: The Fourier transform of a function f(t) is F(ω)=∫−∞∞f(t)e−2πiωtdt, where F(ω) is the frequency domain representation of the given function. Learn & solve Fourier Transforms related problems with SolveletAI advanced step-by-step solution. Generated instantly, learn and get explanations of the problem with Fourier Transforms calculator at SolveletAI.

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