A variational method for designing adaptive bandlimited wavelets

Bahrampour, A. R ; Sharif University of Technology | 2009

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  1. Type of Document: Article
  2. DOI: 10.1007/s11760-008-0077-0
  3. Publisher: 2009
  4. Abstract:
  5. This paper proposes a new method of estimating an orthogonal bounded spectrum wavelet from a given signal. The method is based on minimizing the distance of the wavelet and the given signal in the sense of the metric of the L2 space. In this method, the amplitude and phase of the mother wavelet are optimized simultaneously. The Lagrange multipliers technique is applied to consider the constraints due to the bounded spectrum wavelet and orthogonality conditions. The variational method reduced the optimal matching problem to the solution of a set of functional equations for the amplitude and phase of the optimal-matched bandlimited wavelet spectrum. Continuous functional equations are written with respect to Fourier coefficients of phase of transfer function of the quadrate low-pass filter at the sampled frequencies, and asset of discrete algebraic equations allows us to design the wavelet directly from the signal of interest. To demonstrate the performance of the presented method in this paper, it is employed to determine the matched wavelets of some specified signals. © Springer-Verlag London Limited 2008
  6. Keywords:
  7. Bandlimited wavelets ; Matched wavelet ; Variational methods ; Algebraic equations ; Bandlimited ; Continuous functionals ; Fourier coefficients ; Functional equation ; Mother wavelets ; Optimal matching ; Orthogonality conditions ; Signal of interests ; Functional analysis ; Lagrange multipliers ; Low pass filters ; Optimization ; Ordinary differential equations ; Signal processing
  8. Source: Signal, Image and Video Processing ; Volume 3, Issue 4 , 2009 , Pages 363-374 ; 18631703 (ISSN)
  9. URL: https://link.springer.com/article/10.1007/s11760-008-0077-0