Optimal sampling of non band-limited functions is an issue of great importance that has attracted considerable attention. We propose to tackle this problem through the use of a frequency warping: First, by a non-linear shrinking of frequencies, the function is transformed into a band-limited one. One may then perform a decomposition in Fourier series. This process gives rise to new orthonormal ...

Abstract There has re ently been interest in the use of orthonormal bases for the purposes of SISO system identi ation. Con urrently, but separately, there has also been vigorous work on estimation of MIMO systems by omputationally heap and reliable s hemes. These latter ideas have olle tively be ome known as `4SID' methods. This paper is a ontribution overlapping these two s hools of thought b...

We describe extensions to the \best-basis" method to select orthonormal bases suitable for signal classiica-tion and regression problems from a large collection of orthonormal bases. For classiication problems, we select the basis which maximizes relative entropy of time-frequency energy distributions among classes. For regression problems, we select the basis which tries to minimize the regres...

The most simple (and useful) linear expansions for Hilbert spaces are the ones that are based on orthonormal bases. Recall that a set of vectors {xα} in an inner product space (IPS) X is said to be orthogonal if xα ⊥ xβ whenever α 6= β. In addition, if each vector in the set is normalized to have unit norm then the set is said to be orthonormal. Orthonormal sets have many nice properties that m...

The Balian–Low Theorem is a strong form of the uncertainty principle for Gabor systems which form orthonormal or Riesz bases for L(R). In this paper we investigate the Balian–Low Theorem in the setting of Schauder bases. We prove that new weak versions of the Balian–Low Theorem hold for Gabor Schauder bases, but we constructively demonstrate that several variants of the BLT can fail for Gabor S...

This article discusses the basic properties of finite-dimensional Boolean vector spaces and their linear transformations. We first introduce a natural Boolean-valued inner product and discuss orthonormal bases. We show that all bases are orthonormal and have the same cardinality. It is shown that the set of subspaces form an atomistic orthomodular poset. We then demonstrate that an operator tha...