Prove the convolution of f and g

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Start date Aug 2, 2012
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Convolution

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SUMMARY

The discussion centers on proving the convolution of two functions, f and g, through the application of the Fourier transform. The integral to evaluate is $$\int_{-\infty}^{\infty}f(x-y)g(y)dy$$, which requires transforming it into a double integral. A change of variables is essential to separate the integrals effectively, facilitating the proof of the convolution theorem.

PREREQUISITES

Understanding of Fourier transforms
Knowledge of convolution operations
Familiarity with integral calculus
Experience with change of variables in integrals

NEXT STEPS

Study the properties of Fourier transforms
Learn about convolution in the context of signal processing
Explore techniques for changing variables in integrals
Investigate applications of convolution in differential equations

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Students in mathematics, engineers working with signal processing, and anyone interested in understanding the convolution of functions through Fourier analysis.

Aug 2, 2012

abstracted6

This was the bonus question on my test, I couldn't really figure out how to begin.

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Aug 2, 2012

LCKurtz

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Homework Helper

Start by writing the Fourier transform of$$
\int_{-\infty}^{\infty}f(x-y)g(y)dy$$
It will be an integral of that, so it will be a double integral. See if you can find a change of variables that allows you to separate the integrals.