Time

Convolution in time frequency domain

Convolution in time frequency domain
  1. What is convolution in the time domain?
  2. How does convolution behave in time and frequency domain?
  3. Why is the convolution in time domain multiplication in frequency domain?

What is convolution in the time domain?

Convolution is cyclic in the time domain for the DFT and FS cases (i.e., whenever the time domain has a finite length), and acyclic for the DTFT and FT cases. That is, convolution in the time domain corresponds to pointwise multiplication in the frequency domain.

How does convolution behave in time and frequency domain?

Statement - The frequency convolution theorem states that the multiplication of two signals in time domain is equivalent to the convolution of their spectra in the frequency domain.

Why is the convolution in time domain multiplication in frequency domain?

We know that a convolution in the time domain equals a multiplication in the frequency domain. In order to multiply one frequency signal by another, (in polar form) the magnitude components are multiplied by one another and the phase components are added.

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