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.

No abstract

The paper discussed the application of wavelet-based cross-correlation analysis to the processing of the leak noise signals acquired in the field. Nine recordings produced with the commercial leak noise correlator are considered in this study. All the cases are considered as classified as challenging for signal interpretation. For most of the cases, the basic correlation technique proved to be insufficient to measure the time lag with the required confidence. We implemented a wavelet cross-correlation algorithm for time lag estimation. At least in five cases out of nine, it managed to estimate time lag accurately. In three of the remaining cases, it failed. Unfortunately, due to a lack of information on field studies when records were produced, we are not able to investigate the reason of failures. We concluded that the proposed solution is practical and can be implemented in the software of leak noise correlators.