Fft convolution

1. What is FFT convolution?
2. Why is FFT faster than convolution?
3. Is DFT a convolution?
4. What is convolution in frequency domain?

What is FFT convolution?

FFT convolution uses the principle that multiplication in the frequency domain corresponds to convolution in the time domain. The input signal is transformed into the frequency domain using the DFT, multiplied by the frequency response of the filter, and then transformed back into the time domain using the Inverse DFT.

Why is FFT faster than convolution?

The convolution uses your O(n) per output sample. But because the FFT over 2n points coughs up 2n points, and n of those points are 'new', you only do the FFT 1/n as many times as you'd do the convolution.

Is DFT a convolution?

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.

What is convolution in frequency domain?

A convolution operation is used to simplify the process of calculating the Fourier transform (or inverse transform) of a product of two functions. When you need to calculate a product of Fourier transforms, you can use the convolution operation in the frequency domain.