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Megatron16
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Can anybody help in in finding the Fourier transform of f(x) = xe^-x where -1<x<0 and f(x)= 0 otherwise?
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The Fourier Transform of xe^-x is 1/(1+iw)^2, where w represents the frequency variable.
To find the Fourier Transform of xe^-x, you can use the formula F(w) = ∫ ∞ -∞ f(x)e^-iwx dx, where f(x) is the function xe^-x and w is the frequency variable.
The Fourier Transform of xe^-x is important because it allows us to convert a function from the time domain to the frequency domain. This can be useful in various fields, such as signal processing and image processing.
Yes, the Fourier Transform of xe^-x can be easily calculated using computer software, such as MATLAB or Python, which have built-in functions for calculating Fourier Transforms.
Yes, the Fourier Transform of xe^-x is used in various applications, such as analyzing signals in communication systems, removing noise from images, and solving differential equations in engineering and physics problems.