Acoustic signal representations used in current audio coding algorithms can be improved by the incorporation of biorthogonality into Malvar's Extended Lapped Transform (ELT). Biorthogonality allows more exibility in the design of the analysis and synthesis windows by increasing the number of degrees of freedom. This paper examines this increase for two special cases and demonstrates the importa...

The Askey-Wilson polynomials are orthogonal polynomials in x = cos θ, which are given as a terminating 4φ3 basic hypergeometric series. The non-symmetric AskeyWilson polynomials are Laurent polynomials in z = eiθ, which are given as a sum of two terminating 4φ3’s. They satisfy a biorthogonality relation. In this paper new orthogonality relations for single 4φ3’s which are Laurent polynomials in...

In this letter, the two wavelet families, biorthogonal and Riesz bases are introduced. Biorthogonality for two possible decompositions in these bases, The Riesz stability implies that there exist such that Biorthogonal wavelet bases are related to multiresolution approximations. The direct consequence of the above derivation is tradeoff made between the support size of a wavelet and its number ...

In this work, a class of multivariate multiwavelet packages with multi-scale are introduced, which are generalizations of multivariant wavelet packages. A method for designing a sort of biorthogonal multiwavelet packages in higher dimensions is presented and their biorthogonality property is characterized by virtue of time-frequency analysis method, matrix theory, and operator theory. Three bio...

The purpose of this note is to illustrate the use of step-indexing [2] combined with biorthogonality [10, 9] to construct syntactical logical relations. It walks through the details of a syntactically simple, yet non-trivial example: a proof of the “CIU Theorem” for contextual equivalence in the untyped call-by-value λ-calculus with recursively defined functions. I took as inspiration two works...

We use the framework of biorthogonality to introduce a novel semantic definition of the concept of barb (basic observable) for process calculi. We develop a uniform basic theory of barbs and demonstrate its robustness by showing that it gives rise to the correct observables in specific process calculi which model synchronous, asynchronous and broadcast communication regimes.