The convolution theorem says that convolution in an image domain is equivalent to a simple multiplication in the frequency domain:

Following diagram shows the application of fourier transforms:

The next diagram shows the basic steps in frequency domain filtering. We have the original image, F, and a kernel (a mask or a degradation/enhancement function) as input. First, both input items need to be converted into the frequency domain with DFT, and then the convolution needs to be applied, which by convolution theorem is just an (element-wise) multiplication. This outputs the convolved image in the frequency domain, on which we need to apply IDFT to obtain the reconstructed image (with some degradation or enhancement on the original image):

Let's now see the demonstration of the theorem on a few images and with a few Python library functions. We need to import all of the required libraries just as we did in the last chapter.