A contiguous relation for complementry pairs of very well poised balanced 10φ9 basic hypergeometric functions is used to derive an explict expression for the associated continued fraction. This generalizes the continued fraction results associated with both Ramanujan’s Entry 40 and Askey-Wilson polynomials which can be recovered as limits. Associated with our continued fraction results there ar...

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In 1917, D'Arch Thompson suggested that one should study the change from one biological form to another by examining the unique mathematical object that maps between them in accord with biological homologies. Biorthogonal grids provide a particular coordinate system for visualizing such a map and lead to a quantitative syntax in which a change in shape is reduced to differential changes in size...

Finding a good wavelet for a particular application and type of input data is a difficult problem. Traditional methods of wavelet design focus on abstract properties of the wavelet that can be optimized analytically but whose influence on its real-world performance are not entirely understood. In this paper, a coevolutionary genetic algorithm is developed that searches the space of biorthogonal...

Abstract. Let f ∈ Lp(R), 1 ≤ p < ∞ and let Λ ⊆ R be discrete. We consider the nature of the closed linear span X of the translations of f by λ ∈ Λ under the assumption that these translations can be ordered to be basic, unconditional basic, a Schauder frame or a biorthogonal system. We show, for example, that such a system can never be a basis for L1(R) or an unconditional basis for Lp(R) if 1 ...

In this paper, we propose and analyze concatenated coding schemes for direct-sequence code-division multiple-access (DS/CDMA) systems in asynchronous channels. In the concatenated coding, bandwidth-efficient 2 -state L/(L+1)-rate 2MTCM with biorthogonal signal constellation is used for the inner code, and (2 1, d(2 1)/L/2e) RS code is used for the outer code. It is shown that we can get conside...

Keywords: Biorthogonal transform Image compression JPEG algorithm All phase biorthogonal transform (APBT) Dual biorthogonal basis vectors Walsh transform (WT) Discrete cosine transform (DCT) Inverse discrete cosine transform (IDCT) Peak signal to noise ratio (PSNR) a b s t r a c t This paper proposes new concepts of the all phase biorthogonal transform (APBT) and the dual biorthogonal basis vec...

Downsampling and upsampling are widely used in image display, compression, and progressive transmission. In this paper we examine new down/upsampling methods using frequency response analysis and experimental evaluation. We consider six classes of filters for down/upsampling: decimation/duplication, bilinear interpolation, least-squares filters, orthogonal wavelets, biorthogonal wavelets, and a...