A discrete-time multiresolution theory

The theory of matrix-valued multiresolution analysis frames

A Quantitative Analysis of an EEG Epileptic Record Based on MultiresolutionWavelet Coefficients

The characterization of the dynamics associated with electroencephalogram (EEG) signal combining an orthogonal discrete wavelet transform analysis with quantifiers originated from information theory is reviewed. In addition, an extension of this methodology based on multiresolution quantities, called wavelet leaders, is presented. In particular, the temporal evolution of Shannon entropy and the...

Nonlinear Filtering of Time Series Using the Wavelet Transform

A fast nonlinear filtering algorithm is presented. This algorithm propagates the entire conditional probability functions recursively in a computationally efficient manner using the discrete wavelet transform. With the multiresolution analysis capability offered by the wavelet transform we can speed up the computation by ignoring the high-frequency details of the probability function up to a ce...

Wavelet transforms associated with finite cyclic groups

AbstmctMultiresolution analysis via decomposition on wavelet bases has emerged as an important tool in the analysis of signals and images when these objects are viewed as sequences of complex or real numbers. An important class of multiresolution decompositions are the so-called Laplacian pyramid schemes, in which the resolution is successively halved by recursively lowpass filtering the signal...

Pole Assignment Of Linear Discrete-Time Periodic Systems In Specified Discs Through State Feedback

The problem of pole assignment, also known as an eigenvalue assignment, in linear discrete-time periodic systems in discs was solved by a novel method which employs elementary similarity operations. The former methods tried to assign the points inside the unit circle while preserving the stability of the discrete time periodic system. Nevertheless, now we can obtain the location of eigenvalues ...