provide an accessible introduction to Fourier analysis and its applications." - from Discrete Fourier Transform ,In this chapter, we can peek into the FFT/DFT via the examples for sine wave, square wave, and unit pulse. The DFT has become a mainstay of numerical computing in part because of a very fast algorithm for computing it, called the Fast Fourier Transform (FFT), which was known to Gauss (1805) and was brought to light in its current form by Cooley and Tukey. The derivative would be zero, except where the square wave changes value when it would jump to +/- infinity, theoretically, though in practise it would just a very high value. ,"When both the function and its Fourier transform are replaced with discretized counterparts, it is called the discrete Fourier transform (DFT). First, we will need an input time array to create our square wave. The Discrete Fourier Transform (DFT) is used to determine the frequency content of signals and the Fast Fourier Transform (FFT) is an efficient method for calculating the DFT. Let us see how the code for creating square wave looks like in MATLAB: Example 1. A fast Fourier transform (FFT) is a method to calculate a discrete Fourier transform (DFT).,Spectral analysis is the process of determining the frequency domain representation of a signal in time domain and most commonly employs the Fourier transform.
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