ABSTRACT
The use of orthogonal functions greatly simplifies the process of finding a least-squares fit of a linear function to a set of data. The Fourier series is an important example of a linear least-squares function, and the Fourier series is a series made up of orthogonal functions. This chapter reviews three topics least squares, orthogonality, and the Fourier series have been fundamental to digital signal processing (DSP) since its beginning. An understanding of these subjects provides insight into almost every area of spectral analysis and DSP system design. The principle of least squares is used often in DSP with signals and other functions of one or more variables. In DSP, least-squares approximations are made more often to discrete (sampled) data rather than to continuous data. In addition to the principle of least squares, orthogonality is another important concept often used in DSP.
