How to zero pad a 3d data and apply fast convolution?

1. What are the methods of fast convolution?
2. Why do we use zero padding in circular convolution?
3. Is zero padding is mandatory for both linear and circular convolution?
4. Why is it necessary to pad an image with zeros before computing its DFT?

What are the methods of fast convolution?

Fast convolution can be carried out using FFTs. Take the FFT of both input signals (with appropriate zero padding), multiply in the frequency domain, then do an inverse FFT. For large N (typically N > 100) this is faster than the direct method.

Why do we use zero padding in circular convolution?

The method of extending signals by adding zeros is known as zero padding . If three zeros are added to each of the signals and then a circular convolution is performed, the result is the same as that of a linear convolution.

Is zero padding is mandatory for both linear and circular convolution?

The linear convolution of an N-point vector, x , and an L-point vector, y , has length N + L - 1. For the circular convolution of x and y to be equivalent, you must pad the vectors with zeros to length at least N + L - 1 before you take the DFT.

Why is it necessary to pad an image with zeros before computing its DFT?

If one has any interest in the spectrum of the windowing function used to isolate the time-domain sample, then zero-padding WILL increase the frequency resolution of the windowing function.