The goal of this exercise is to determine the Fourier transform of the function𝑓(𝑥)={𝑥if −1<𝑥<10otherwisef(x)={ x0 if −1<x<1otherwise
Question
Solution 1
The Fourier transform of a function f(x) is given by the integral:
F(k) = ∫ f(x) e^(-2πikx) dx
In this case, the function f(x) is x for -1 < x < 1 and 0 otherwise. So, we only need to consider the interval from -1 to 1 in the integral. Therefore, the Fourier transform is:
F(k) = ∫_{-1}^{1} x e^(- Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
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