Nonorthogonal signal decomposition.

A New Method for Nonorthogonal Signal Decomposition1

ing with finite dimensional Gabor sets. Here we describe an iterative method which allows us to perform the decomposition for finite dimensional nonorthogonal sets including Gabor sets. The method is optimal and always stable in the sense that the minimum mean squared error, that is, the norm of the difference between the original function and the reconstructed one, obtained by this method tend...

Nonorthogonal bases and phase decomposition: Properties and applications

In a previous paper (Vergara, S., On Generic Frequency Decomposition. Part 1: Vectorial Decomposition. Dig. Sig. Proc. Vol. 17 N. 2 2007) it was discussed the viability of functional analysis using as a basis a couple of generic functions, and hence vectorial decomposition. Here we complete the paradigm exploiting one of the analysis methodologies developed there, but applied to phase coordinat...

Sparse signal decomposition for periodic signal mixtures

Periodicities are found in speech signals, musical rhythms, biomedical signals and machine vibrations. In many signal processing applications, signals are assumed to be periodic or quasi-periodic. Especially in acoustic signal processing, signal models based on periodicities have been studied for speech and audio processing. The sinusoidal modelling has been proposed to transform an acoustic si...

1 Multiresolution Signal Decomposition Schemes

In its original form, the wavelet transform is a linear tool. However, it has been increasingly recognized that nonlinear extensions are possible. A major impulse to the development of nonlinear wavelet transforms has been given by the introduction of the lifting scheme by Sweldens. The aim of this report, which is a sequel to a previous report devoted exclusively to the pyramid transform, is t...

Decaying Exponentials and Signal Decomposition