Wavelet analysis [for signal processing]

As every engineering student knows, any signal can be portrayed as an overlay of sinusoidal waveforms of assorted frequencies. But while classical analysis copes superbly with naturally occurring sinusoidal behavior-the kind seen in speech signals-it is ill-suited to representing signals with discontinuities, such as the edges of features in images. Latterly, another powerful concept has swept applied mathematics and engineering research: wavelet analysis. In contrast to a Fourier sinusoid, which oscillates forever, a wavelet is localized in time-it lasts for only a few cycles. Like Fourier analysis, however, wavelet analysis uses an algorithm to decompose a signal into simpler elements. Here, the authors describe how localized waveforms are powerful building blocks for signal analysis and rapid prototyping-and how they are now available in software toolkits.