\If it is true, it can be proved." | Enrico Fermi ABSTRACT. The Balian{Low theorem (BLT) is a key result in time-frequency analysis, originally stated by Balian and, independently, by Low, as: If a Gabor system fe 2imbt g(t ? na)g m;n2Z with ab = 1 forms an orthonormal basis for L 2 (R), then Z 1 ?1 jtg(t)j 2 dt Z 1 ?1 j ^ g()j 2 dd = +1: The BLT was later extended from orthonormal bases to exa...

We show that the homogeneous approximation property and the comparison theorem hold for arbitrary coherent frames. This observation answers some questions about the density of frames that are not covered by the theory of Balan, Casazza, Heil, and Landau. The proofs are a variation of the method developed by Ramanathan and Steger. Frames provide redundant non-orthogonal expansions in Hilbert spa...

Frames have applications in numerous fields of mathematics and engineering. The fundamental property of frames which makes them so useful is their overcompleteness. In most applications, it is this overcompleteness that is exploited to yield a decomposition that is more stable, more robust, or more compact than is possible using nonredundant systems. This work presents a quantitative framework ...

There are a finite number of inequivalent isometric frames (equal–norm tight frames) of n vectors for C| which are generated from a single vector by applying an abelian group G of symmetries. Each of these so-called harmonic frames can be obtained by taking d rows of the character table of G; often in many different ways, which may even include using different abelian groups. Using an algorithm...

This work presents a quantitative framework for describing the overcompleteness of a large class of frames. It introduces notions of localization and approximation between two frames F = {f i } i∈I and E = {e j } j∈G (G a discrete abelian group), relating the decay of the expansion of the elements of F in terms of the elements of E via a map a : I → G. A fundamental set of equalities are shown ...

In this paper, a packet loss concealment (PLC) algorithm for CELP-type speech coders is proposed in order to improve the quality of decoded speech under burst packet loss conditions in a wireless sensor network. Conventional receiver-based PLC algorithms in the G.729 speech codec are usually based on speech correlation to reconstruct the decoded speech of lost frames by using parameter informat...

$K$-frames which are generalization of frames on Hilbert spaces‎, ‎were introduced‎ ‎to study atomic systems with respect to a bounded linear operator‎. ‎In this paper‎, ‎$*$-$K$-frames on Hilbert $C^*$-modules‎, ‎as a generalization of $K$-frames‎, ‎are introduced and some of their properties are obtained‎. ‎Then some relations‎ ‎between $*$-$K$-frames and $*$-atomic systems with respect to a...

Extending and improving the concepts: woven frame and fusion frames, we introduce the notion of woven fusion frames in Hilbert spaces. We clarify our extension and generalization by some examples of woven frames and woven fusion frames. Also, we present some properties of woven fusion frames, especially we show that for given two woven frames of sequences, one can build woven fusion frames and ...

Fusion frames are valuable generalizations of discrete frames. Most concepts of fusion frames are shared by discrete frames. However, the dual setting is so complicated. In particular, unlike discrete frames, two fusion frames are not dual of each other in general. In this paper, we investigate the structure of the duals of fusion frames and discuss the relation between the duals of fusion fram...

This paper describes extensions of the 4 kb/s hybrid MELP/CELP coder, up to 6.4 kb/s and down to 2.4 kb/s. The baseline 4 kb/s coder uses three coding modes: MELP in strongly voiced speech frames, CELP with pitch prediction in weakly voiced frames, and CELP with stochastic excitation in unvoiced frames. To minimize switching artifacts between parametric MELP and waveform CELP coding, an alignme...