This book is about filter banks and wavelets. Those are new ways to see and represent signal. They are alternatives to the Fourier transform, using short wavelets insted of long wavelets. We will explain the advantages (and disadvantages!) of the new methods. The final decision will depend on the application itself, the actual signal, and its bandwith. To design and understand wavellets we still use Fourier techniques - the connection between time and frequency. This idea remains at the center of signal processing. Wavelets are "alternatives" rather than replacemets. The classical transforms will survive very well. But the ideas have come quickly forward, to be understood and applied.