Wavelet transform-based cross-correlation in the time-delay estimation applications

Abstract

The article discusses the application of wavelet analysis for the time-frequency time-delay estimation. The proposed algorithm is wavelet transform-based cross-correlation time delay estimation that applies discrete time wavelet transform to filter the input signal prior to computation of cross-correlation function. The distinguishing feature of the algorithm that it uses the variation of continuous wavelet transform to process the discrete signals instead of dyadic wavelet transform that is normally applied to the case. Another feature that the implication of convolution theorem is used to compute coefficients of the wavelet transform. This makes possible to omit redundant discrete Fourier transforms and significantly reduce the computational complexity. The principal applicability of the proposed method is shown in the course of a computational experiments with artificial and real-world signal. So the method demonstrated expected selectivity for the signals localized in the different frequency bands. The application of the method to practical case of pipeline leak detection was also successful. However, the study concluded that this method provides no specific advantages in comparison with the conventional one. In the future, alternative applications in biological signal processing will be considered.

Towards applicability of wavelet-based cross-correlation in locating leaks in steel water supply pipes

“…In this paper, we studied the practical applicability of the WCC algorithm proposed and described in [19]. The study confirmed that the WCC method can make a useful tool in the leak noise correlator software.…”

“…For signal processing, the mathematical apparatus of continuous wavelet transform (CWT) was applied. The implementation of CWT to correlation analysis of time series is described in more detail in [19]. The signal processing algorithm is briefly introduced and explained in the final part of this section.…”

“…The algorithm used for the computation of the WCC function is based on the time-frequency correlation analysis technique described in [20] and on a technique of precomputation of discrete filters banks corresponding to the type of the mother wavelet proposed in [21]. A detailed justification and demonstration of the used algorithm are presented in [19]. This subsection is a brief description of it.…”

“…nonoverlapping segments with N ticks in each one. In the equation above, floor brackets denote the rounding to the closest smaller integer value.To compute the WCC we use the formula below for various scale factors m =0, 1, …, M-1[19] …”