Chapter 2. Sampling, Fourier Transform, and Convolution

In this chapter, we'll discuss 2D signals in the time and frequency domains. We'll first talk about spatial sampling, an important concept that is used in resizing an image, and about the challenges in sampling. We'll try solving these problems using the functions in the Python library. We'll also introduce intensity quantization in an image; intensity quantizing means how many bits will be used to store a pixel in an image and what impact it will have on the quality of the image. You will surely want to know about the Discrete Fourier Transform (DFT) that can be used to transform an image from the spatial (time) domain into the frequency domain. You'll learn to implement DFT with the Fast Fourier Transform (FFT) algorithm using numpy and scipy functions and will be able to apply this implementation on an image!

You will also be interested in knowing about 2D convolutions that increase the speed of convolution. We'll also understand...