This detail-oriented text is intended for engineers and applied mathematicians who must write computer programs to perform wavelet and related analyses on real data. It should also be useful to the pure mathematician with questions about wavelet theory applications and to the instructor as a textbook in the mathematics and latest techniques of transient signal analysis and processing. Beginning with an overview of mathematical prerequisites, successive chapters rigorously examine the properties of waveforms used in adapted wavelet analysis: discrete "fast" Fourier transforms, orthogonal and biorthogonal wavelets, wavelet packets, and localized trigonometric or lapped orthogonal functions. Other chapters discuss the "best-basis" method, time-frequency analysis, and combinations of these algorithms useful for signal analysis, denoising, and data compression. Each chapter discusses the technical aspects of implementation, giving examples in pseudocode backed up with a Standard C source code (available on optional diskette), and closes with a list of worked exercises.