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A variational method for designing wavelets to match a specified signal
, Article Signal Processing ; Volume 88, Issue 10 , 2008 , Pages 2417-2424 ; 01651684 (ISSN) ; Izadnia, S ; Vahedi, M ; Sharif University of Technology
Elsevier
2008
Abstract
In this paper, we have developed an efficient method for obtaining an orthonormal wavelet that is matched to a given signal. The error between the wavelet and the given signal is minimized subject to the constraints of the amplitude and phase of the band-limited wavelet spectrum. To consider the constraints of the minimization problem, the Lagrange multipliers technique is applied. Variational method reduced the optimal matching problem to the solution of a set of functional equations for the amplitude and phase of the wavelet spectrum. Continuous functional equations were written in terms of Fourier coefficients of the phase of the transfer function of the quadrature low pass filter at the...