This module relates circular convolution of periodic signals in the time domain to multiplication in the frequency domain.

Inside Collection (Course): Signals and Systems

Summary: This module looks at the basic circular convolution relationship between two sets of Fourier coefficients.

This module relates circular convolution of periodic signals in the time domain to multiplication in the frequency domain.

Given a signal

Circular convolution in the time domain is equivalent to
multiplication of the Fourier coefficients.

Take a look at a square pulse with a period of T.

For this signal

Take a look at a triangle pulse train with a period of T.

This signal is created by circularly convolving the square pulse with itself. The Fourier coefficients for this signal are

Find the Fourier coefficients of the signal that is created when the square pulse and the triangle pulse are convolved.

Circular convolution in the time domain is equivalent to multiplication of the Fourier coefficients in the frequency domain.

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Comments:"My introduction to signal processing course at Rice University."