An irregular sampling algorithm adapted to the local frequency content of signals and the corresponding on-line reconstruction algorithm

The description of signals using wavelet transforms leads to useful time-frequency localization and possible signal compression. Based on the discrete wavelet transform (DWT) an adaptive sampling algorithm in the discrete time domain is constructed, by finding an univocal relation between the signal's samples and the non-zero transform coefficients of its DWT. Reconstruction is performed through repeated projections of an approximation of the initial signal based on the arriving samples, into the original signal's subspace, using the Neumann method of inverting bounded operators. Both adaptive sampling and reconstruction are on-line because of the finite support of the analyzing wavelets.