ABSTRACT
In this chapter, the author examines a new way of decomposing a signal into simpler signals, each of which is a sinusoid. It focuses on the most fundamental and popular technique for spectral analysis—the Discrete Fourier Transform (DFT). DFT provides one of the most popular tools for spectral analysis of visual signals using data independent or standard basis functions. DFT is a technique that takes as input a periodic signal of infinite length and decomposes it into a set of sine and cosine waves which when combined would provide the periodic signal itself. A multitude of software can perform this DFT, but it is important to interpret the results of DFT. DFTs can be extended to higher dimension and they are surprisingly widespread in their use. The Fourier transform has even been used to identify a counterfeit Jackson Pollock painting by deciphering the chemicals in the paint.
