ABSTRACT
This chapter starts with two methods for finding roots via trial-and-error searching. It discusses problems dealing with Fourier analysis and its implementation as the discrete Fourier transform (DFT) algorithm. The chapter also discusses the industrial-strength version of DFT known as the fast Fourier transform. It shows two methods that use Fourier analysis to reduce noise in signals. The chapter describes industrial-strength multi-resolution wavelet analysis. Wavelet analysis extends the short-time Fourier transform idea by using basis functions that oscillate for only a short period of time. The chapter also describes principal components analysis (PCA), a powerful tool for analyzing complex and large data sets, and for extracting space-time correlations. PCA is a powerful tool for deducing and ordering the dominate functions in complicated signals, such as those arising from nonlinear and multiple variable systems. The chapter concludes with the determination of the fractal dimension of an object.
