Wavelet Orthonormal Basis

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Cai Zhanyu - One of the best experts on this subject based on the ideXlab platform.

  • Complexity analysis of Wavelet Orthonormal Basis
    ICSP '98. 1998 Fourth International Conference on Signal Processing (Cat. No.98TH8344), 1998
    Co-Authors: Liu Jiancheng, Cai Zhanyu
    Abstract:

    The signal on a Wavelet Orthonormal Basis of L/sup 2/(R/sup n/), a family Wavelet Orthonormal Basis of function in L/sup 2/(R/sup n/) (/spl radic/2/sup j/, /spl psi/(2/sup j/x-n))/sub (j,n)/spl isin/2j/, is built by dilating and translating a unique function /spl psi//sub x/. However in the finite interval with a boundary, the Wavelet decomposition is not as accurate as we anticipate, f/sub -1/(t) and g/sub -1/(t) are not Orthonormal, so reconstruction is also distortion. Thus to produce a new improved Orthonormal Basis, it would help to process the Wavelet signal.

Liu Jiancheng - One of the best experts on this subject based on the ideXlab platform.

  • Complexity analysis of Wavelet Orthonormal Basis
    ICSP '98. 1998 Fourth International Conference on Signal Processing (Cat. No.98TH8344), 1998
    Co-Authors: Liu Jiancheng, Cai Zhanyu
    Abstract:

    The signal on a Wavelet Orthonormal Basis of L/sup 2/(R/sup n/), a family Wavelet Orthonormal Basis of function in L/sup 2/(R/sup n/) (/spl radic/2/sup j/, /spl psi/(2/sup j/x-n))/sub (j,n)/spl isin/2j/, is built by dilating and translating a unique function /spl psi//sub x/. However in the finite interval with a boundary, the Wavelet decomposition is not as accurate as we anticipate, f/sub -1/(t) and g/sub -1/(t) are not Orthonormal, so reconstruction is also distortion. Thus to produce a new improved Orthonormal Basis, it would help to process the Wavelet signal.

Tohid Aribi - One of the best experts on this subject based on the ideXlab platform.

  • signal approximation with fourier transform based on scaling Orthonormal Basis function
    Research & Reviews: Journal of Engineering and Technology, 2014
    Co-Authors: Tohid Aribi
    Abstract:

    In this paper, we study the properties of the transform which approximates a signal at a given resolution. We show that the difference of a signal at different resolutions can be extracted by decomposing the signal on a Wavelet Orthonormal Basis. In Wavelet Orthonormal Basis is a family of functions, which is built by dilating and translating a unique function. The development of Orthonormal Wavelet bases has opened a new bridge between approximation theory and signal processing. It is possible to keep the simplicity while improving the performance with non-linearities in a sparse representation. The analysis results imply that proposed method has lots of efficiency over other methods.