On discrete-amplitude multiresolution analysis

A new concept named discrete-amplitude multiresolution (DAM) is proposed, in which the representation precision of the signal amplitude is taken as its scale. The discrete multiresolution algorithms presented in the references and are classified into two broad types, frequency-decomposition and time-decomposition. However, the DAM is a kind of code-decomposition. The DAM decomposition in some local segments of a signal behaves like certain self-similar tilings at reasonable scales, and this provides a basis for signal compression. A theorem for reconstructing a signal from its 2-bits binary representation is devised. Finally, examples of applications of the DAM to digital signal processing is discussed and some attractive features of the DAM implementation are revealed, such as the computational simplicity, parallel processing, and quantization-error free.