A dimension invariance property of finite frames of translates and Gabor frames is discussed. Under appropriate support conditions among the frame and dual frame generating functions, we show that a pair of dual frames evaluated in a given space remains a valid dual set if they are naturally embedded in the underlying space of almost arbitrarily enlarged dimension. Consequently, the evaluation ...

In this note we will show that the so called Sobolev dual is the minimizer over all linear reconstructions using dual frames for stable r order Σ∆ quantization schemes under the so called White Noise Hypothesis (WNH) design criteria. We compute some Sobolev duals for common frames and apply them to audio clips to test their performance against canonical duals and another alternate dual correspo...

For X a compact abelian group and B an infinite subset of its dual X̂, let CB be the set of all x ∈ X such that 〈φ(x) : φ ∈ B〉 converges to 1. If F is a free filter on X̂, let DF = {CB : B ∈ F}. The sets CB and DF are subgroups of X. CB always has Haar measure 0, while the measure of DF depends on F . We show that there is a filter F such that DF has measure 0 but is not contained in any CB . Thi...

Recently, research on two distinct types of wavelet frames have emerged, each with its own characteristics. The dual-tree discrete wavelet transform (DWT) [1] is based on the concatenation of two wavelet bases, where the two wavelets are designed to form a Hilbert transform pair, Ãg(t) = HfÃh(t)g [4]. A second type of wavelet frame is based on a single scaling function and two distinct wavelets...

Approximately dual frames as a generalization of duality notion in Hilbert spaces have applications Gabor systems, wavelets, coorbit theory, and sensor modeling. In recent years, the computing associated deviations canonical alternate from original ones has been considered by functional analysts. this paper, we consider quantitative measurement approximately ones. More precisely, it is proved t...

We introduce observation frames as an extension of ordinary frames. The aim is to give an abstract representation of a mapping from observable predicates to all predicates of a specific system. A full subcategory of the category of observation frames is shown to be dual to the category of F! topological spaces. The notions we use generalize those in the adjunction between frames and topological...

In this article, we discuss some recent developments on pairs of dual wavelet frames in Sobolev spaces constructed by the Oblique Extension Principle (OEP) from refinable function vectors. Our investigation sheds a new light on understanding the OEP method for constructing MRA dual wavelet frames.

The noisy short utterance is polluted by noise and corpus is less, so the recognition rate significantly decreased. For improving recognition rate, we proposed the dual information quality discrimination algorithm to classify the speech frames: one is differences detection and discrimination algorithm (DDADA), another is the improved SNR discrimination algorithm (ISNRDA). Based on the above two...