We consider the modeling of non-stationary discrete signals whose amplitude and frequency are assumed to be nonlinearly modulated over very short-time duration. We investigate the case where both instantaneous amplitude and frequency can be approximated by orthonormal polynomials. Previous works dealing with polynomial approximations refer to orthonormal bases built from a discretization of con...

This discussion sparse representations of signals in R. The sparsity of a signal is quantified by the number of nonzero components in its representation. Such representations of signals are useful in signal processing, lossy source coding, image processing, etc. We first speak of an uncertainty principle regarding the sparsity of any two different orthonormal basis representations of a signal S...

In this report we present a collection of results concerning two families of rational orthonormal functions, one on the unit circle, and another on the imaginary axis. We also describe in detail an interesting link between the two families. Special cases of these rational orthonormal functions include the Laguerre and Kautz orthonormal functions, as well as the orthonormal functions recently in...

In this paper an algorithm and architecture for computing the eigenvalue decomposition (EVD) of a symmetric matrix is presented. The EVD is computed using a Jacobi-type method, where the angle of the rotations is approximated by an angle k , corresponding to an orthonormal {rotation. These orthonormal {rotations are based on the idea of CORDIC and share the property that performing the rotation...

Theory of optimal orthonormal filter banks has recently been developed under the assumption that quantizers operate at high bit rates. We show that the theory can be simplified if a more general model for quantizers is used. With such a model, we show that principal component filter banks (PCFB) are optimal for orthonormal subband coding under all bit rates and bit allocation strategies. This e...