Breeze has several methods to help you write digital signal processing code. These include functions for convolution, Fourier transforms, and several digital filters. These are useful when you are dealing with digital signals, such as sound and others. Anyone working with sound, speech, image processing, and other similar areas, such as pattern recognition, will find these useful. In this section, we will also use Breeze's plotting facilities to help us illustrate some concepts.
Fourier transforms are named after Joseph Fourier, who, in 1822, showed that some functions can be written as the (possibly) infinite sum of harmonics. Getting into the topic of Fourier analysis is out of the scope of this book. It will be assumed that the reader knows what they are and what they are useful for. We will simply show you how to do discrete Fourier transforms using Breeze. Here, we present a program that does a Fourier transform on a simple signal that consists of...