Topic
Biorthogonal system
About: Biorthogonal system is a research topic. Over the lifetime, 2190 publications have been published within this topic receiving 32209 citations.
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TL;DR: In this article, some algorithms for constructing orthogonal and biorthogonal compactly supported wavelets on Vilenkin groups are suggested and several examples of p-adic wavelets, which correspond to the refinable functions presented recently by the first author, are given.
Abstract: In this paper, some algorithms for constructing orthogonal and biorthogonal compactly supported wavelets on Vilenkin groups are suggested. As application, several examples of p-adic wavelets, which correspond to the refinable functions presented recently by the first author, are given.
30 citations
Patent•
04 Sep 2007
TL;DR: LIFTLT as discussed by the authors is a multi-band linear phase lapped biorthogonal transform with fast, VLSI-friendly implementations via lifting steps, which is based on a lattice structure which robustly enforces both linear phase and perfect reconstruction properties.
Abstract: This invention introduces a class of multi-band linear phase lapped biorthogonal transforms with fast, VLSI-friendly implementations via lifting steps called the LiftLT. The transform is based on a lattice structure which robustly enforces both linear phase and perfect reconstruction properties. The lattice coefficients are parameterized as a series of lifting steps, providing fast, efficient in-place computation of the transform coefficients as well as the ability to map integers to integers. Our main motivation of the new transform is its application in image and video coding. Comparing to the popular 8.times.8 DCT, the 8.times.16 LiftLT only requires 1 more multiplication, 22 more additions, and 6 more shifting operations. However, image coding examples show that the LiftLT is far superior to the DCT in both objective and subjective coding performance. Thanks to properly designed overlapping basis functions, the LiftLT can completely eliminate annoying blocking artifacts. In fact, the novel LiftLT's coding performance consistently surpasses that of the much more complex 9/7-tap biorthogonal wavelet with floating-point coefficients. More importantly, our transform's block-based nature facilitates one-pass sequential block coding, region-of-interest coding/decoding as well as parallel processing.
30 citations
27 Nov 2000
TL;DR: A new system of multicarrier modulation is described which takes advantage of the biorthogonality property to generalize the OFDM/OQAM technique into a bIORthogonal frequency division multiplex scheme named BFDM/ OQAM.
Abstract: A new system of multicarrier modulation is described which takes advantage of the biorthogonality property to generalize the OFDM/OQAM technique into a biorthogonal frequency division multiplex scheme named BFDM/OQAM. A discrete-time analysis of this scheme leads to a discrete model of modulated transmultiplexer. Using a polyphase decomposition of this transmultiplexer, and assuming a distortion-free channel, we determine the mathematical conditions on the prototype filter allowing an exact cancellation of intersymbol and interchannel interference. Then, computationally efficient realizations of the modulators and demodulators are given. Lastly, some design examples are provided illustrating respective advantages of BFDM/OQAM and OFDM/OQAM.
30 citations
TL;DR: In both analyzed cases the Fourier characterization of the controllable spaces of initial data and the construction and evaluation of biorthogonal sequences are given and particular controls for them are constructed.
Abstract: The paper studies the controllability properties of the linear 2-D wave equation in the rectangle Ω = (0, a) × (0, b). We consider two types of action, on an edge or on two adjacent edges of the boundary. Our analysis is based on Fourier expansion and explicit construction and evaluation of biorthogonal sequences. This method allows us to measure the magnitude of the control needed for each eigenfrequency. In both analyzed cases we give a Fourier characterization of the controllable spaces of initial data and we construct particular controls for them.
30 citations
TL;DR: Harten's interpolatory multiresolution representation is generalized to include Hermite interpolation with optimal order accuracy, and the resulting multiple basis functions are symmetric or skew-symmetric, compact, and analytic.
Abstract: We generalize Harten's interpolatory multiresolution representation to include Hermite interpolation. Compact Hermite interpolation with optimal order accuracy is used in both the decomposition and reconstruction algorithm. The resulting multiple basis functions (biorthogonal multiwavelets) are symmetric or skew-symmetric, compact, and analytic. Harten's approach has several advantages: the multiresolution scheme is inherently discrete, nonperiodic boundary conditions are easy to implement, and the representation can be extended to nonuniform grids in bounded domains. We demonstrate the compression features of the new multiple basis functions by application to several examples.
30 citations