Harmonic wavelet transform

About: Harmonic wavelet transform is a research topic. Over the lifetime, 9602 publications have been published within this topic receiving 247336 citations.

Dynamic supply current testing of analog circuits using wavelet transform

Abstract: Dynamic supply current (IDD) analysis has emerged as an effective way for defect oriented testing of analog circuits. In this paper, we propose using wavelet decomposition of IDD for fault detection in analog circuits. Wavelet transform has the property of resolving events in both time and frequency domain simultaneously unlike Fourier expansion which localizes a signal in terms of frequency only. Wavelet transform also has better sub-banding property and it can be easily adapted to current waveforms from different circuits. These make wavelet a more suitable candidate for fault detection in analog circuits than pure time-domain or pure frequency-domain methods. We have shown that for equivalent number of spectral components, sensitivity of wavelet based fault detection is much higher than Fourier or time-domain analysis for both catastrophic and parametric faults. Simulation results on benchmark circuits show that wavelet based method is on average 25 times more sensitive than DFT (Discrete Fourier Transform) for parametric faults and can be considered as a promising alternative for analog fault detection amidst measurement hardware noise and process variation.

An approach using wavelet transform for fault type identification in digital relaying

Abstract: This paper proposes the use of wavelet transform (WT) in power transmission lines for identifying fault types. WT multiresolution properties are quite adequate for detection of fast changes contained in the disturbed signal. Wavelet decomposition associated with modal components have shown to be an excellent alternative for quick identification of faulted phases. Digitized phase voltage and/or current signals are fed to wavelet filters. The coefficients obtained are then transformed by a modified modal transformation matrix. From the resulting signals, the energy is measured with short time intervals. With an appropriately chosen threshold the fault type is identified. EMTP simulations are used to test and validate the proposed methodology. The obtained results are encouraging and the proposed technique requires a low computational complexity, allowing it to be used as part of a high speed protective relay.

Construction of a Morlet Wavelet Power Spectrum

Abstract: The Morlet wavelets transform (MWT) is an efficient means of detecting and analyzing transient signals. However, ordinary iterative processes that calculate the MWT are time-consuming. In addition, when the MWT is applied to construct a wavelet power spectrum on a linear frequency axis, the peak response appears at a value lower than the actual signal frequency. In this work, formulae that produce a fast MWT and Morlet power spectrum (MPS) scheme without iterative processes are derived. Also, we discuss in detail why the frequency slant phenomenon occurs. To avert this phenomenon, the transform kernel of the MWT is modified to facilitate the construction of an equal-amplitude Morlet wavelet transform. The modified Morlet power spectrum produces the peak responses roughly proportional to the squared input amplitudes at the accurate signal component frequencies.

Noise reduction in astronomical spectra using wavelet packets

Abstract: The wavelet representation of a signal offers greater flexibility in de-noising astronomical spectra than classical Fourier smoothing due to the additional wavelength resolution of the decomposed signal. We present here a new wavelet-based approach to noise reduction. It is similar to an application of the splitting algorithm of a wavelet packets analysis using non-orthogonal wavelets. It clearly separates the signal from the noise, in particular also at the noise-dominated highest frequencies. This allows a better suppression of the noise, so that the spectrum de-noised in this manner provides a closer approximation of the uncorrupted signal than in the case of a single wavelet transformation or a Fourier transform. We test this method on intensity and circularly polarized spectra of the sun and compare with Fourier and other wavelet-based de-noising algorithms. Our technique is found to give better results than any other tested de-noising algorithm. It is shown to be particularly successful in recovering weak signals that are practically drowned by the noise.

Wavelet transform analysis of dynamic speckle patterns texture

Abstract: We propose the use of the wavelet transform to characterize the time evolution of dynamic speckle patterns. We describe it by using as an example a method used for the assessment of the drying of paint. Optimal texture features are determined and the time evolution is described in terms of the Mahalanobis distance to the final (dry) state. From the behavior of this distance function, two parameters are defined that characterize the evolution. Because detailed knowledge of the involved dynamics is not required, the methodology could be implemented for other complex or poorly understood dynamic phenomena.