Superposition frames for adaptive time-frequency analysis and fast reconstruction

In this article we introduce a broad family of adaptive, linear time-frequency representations termed superposition frames, and show that they admit desirable fast overlap-add reconstruction properties akin to standard short-time Fourier techniques. This approach stands in contrast to many adaptive time-frequency representations in the extant literature, which, while more flexible than standard fixed-resolution approaches, typically fail to provide efficient reconstruction and often lack the regular structure necessary for precise frame-theoretic analysis. Our main technical contributions come through the development of properties which ensure that this construction provides for a numerically stable, invertible signal representation. Our primary algorithmic contributions come via the introduction and discussion of specific signal adaptation criteria in deterministic and stochastic settings, based respectively on time-frequency concentration and nonstationarity detection. We conclude with a short speech enhancement example that serves to highlight potential applications of our approach.Comment: 16 pages, 6 figures; revised versio

Performance Evaluation of Real Power Quality Disturbances Analysis using S-transform

Power quality is main issue because of the impact to electricity suppliers, equipments, manufacturers and user.To solve the power quality problem, an analysis of power quality disturbances is required to identify and rectify any failures on power system. Most of researchers apply fourier transform in power quality analysis, however the ability of fourier transform is limited to spectral information extraction that can be applied on stationary disturbances. Thus, time-frequency analysis is introduced for analyzing the power quality distubances because of the limitation of fourier transform. This paper presents the analysis of real power quality disturbances using S-transform. This time-frequency distribution (TFD) is presented to analyze power quality disturbances in time-frequency representation (TFR). From the TFR, parameters of the disturbances such as instantaneous of root mean square (RMS), fundamental RMS, total harmonic distortion (THD), total nonharmonic distortion (TnHD) and total waveform distortion (TWD) of the disturbances are estimated. The experimental of three phase voltage inverter and starting motor are conducted in laboratory to record the real power quality disturbances. The disturbances are recorded via data logger system which is mplemented using LabVIEW while the analysis is done using Matlab in offline condition. The results show that S-transform gives good performance in identifying, detecting and analyzing the real power quality disturbances, effectively

Co-compact Gabor systems on locally compact abelian groups

In this work we extend classical structure and duality results in Gabor analysis on the euclidean space to the setting of second countable locally compact abelian (LCA) groups. We formulate the concept of rationally oversampling of Gabor systems in an LCA group and prove corresponding characterization results via the Zak transform. From these results we derive non-existence results for critically sampled continuous Gabor frames. We obtain general characterizations in time and in frequency domain of when two Gabor generators yield dual frames. Moreover, we prove the Walnut and Janssen representation of the Gabor frame operator and consider the Wexler-Raz biorthogonality relations for dual generators. Finally, we prove the duality principle for Gabor frames. Unlike most duality results on Gabor systems, we do not rely on the fact that the translation and modulation groups are discrete and co-compact subgroups. Our results only rely on the assumption that either one of the translation and modulation group (in some cases both) are co-compact subgroups of the time and frequency domain. This presentation offers a unified approach to the study of continuous and the discrete Gabor frames.Comment: Paper (v2) shortened. To appear in J. Fourier Anal. App

Estimation of the blood Doppler frequency shift by a time-varying parametric approach

International audienceDoppler ultrasound is widely used in medical applications to extract the blood Doppler flow velocity in the arteries via spectral analysis. The spectral analysis of non-stationary signals and particularly Doppler signals requires adequate tools that should present both good time and frequency resolutions. It is well-known that the most commonly used time-windowed Fourier transform, which provides a time-frequency representation, is limited by the intrinsic trade-off between time and frequency resolutions. Parametric methods have then been introduced as an alternative to overcome this resolution problem. However, the performances of those methods deteriorate when high non-stationarities are present in the Doppler signal. For the purpose of accurately estimating the Doppler frequency shift, even when the temporal flow velocity is rapid (high non-stationarity), we propose to combine the use of the time-varying auto-regressive method and the (dominant) pole frequency. This proposed method performs well in the context where non-stationarities are very high. A comparative evaluation has been made between classical (FFT based) and auto-regressive (both block and recursive) algorithms. Among recursive algorithms we test an adaptive recursive method as well as a time-varying recursive method. Finally, the superiority of the time-varying parametric approach in terms of frequencies tracking and of delay on the frequency estimate is illustrated on both simulated and in vivo Doppler signals

Wigner analysis of operators. Part I: pseudodifferential operators and wave fronts

We perform Wigner analysis of linear operators. Namely, the standard time-frequency representation \emph{Short-time Fourier Transform} (STFT) is replaced by the $\mathcal{A}$-\emph{Wigner distribution} defined by $W_{\mathcal A} (f)=\mu({\mathcal A})(f\otimes\bar{f})$, where ${\mathcal A}$ is a $4d\times 4d$ symplectic matrix and $\mu({\mathcal A})$ is an associate metaplectic operator. Basic examples are given by the so-called $\tau$-Wigner distributions. Such representations provide a new characterization for modulation spaces when $\tau\in (0,1)$. Furthermore, they can be efficiently employed in the study of the off-diagonal decay for pseudodifferential operators with symbols in the Sj\"ostrand class (in particular, in the H\"{o}rmander class $S^0_{0,0}$). The novelty relies on defining time-frequency representations via metaplectic operators, developing a conceptual framework and paving the way for a new understanding of quantization procedures. We deduce micro-local properties for pseudodifferential operators in terms of the Wigner wave front set. Finally, we compare the Wigner with the global H\"{o}rmander wave front set and identify the possible presence of a ghost region in the Wigner wave front. \par In the second part of the paper applications to Fourier integral operators and Schr\"{o}dinger equations will be given.Comment: Improved version. 43 page

On the Grunbaum Commutor Based Discrete Fractional Fourier Transform

The basis functions of the continuous fractional Fourier transform (FRFT) are linear chirp signals that are suitable for time-frequency analysis of signals with chirping time-frequency content. In the continuous--time case, analytical results linking the chirp rate of the signal to a specific angle where the FRET of the chirp signal is an impulse exist. Recent efforts towards developing a discrete and computable version of the fractional Fourier transform (DFRFT) have focussed on furnishing a orthogonal set of eigenvectors for the DFT that serve as discrete versions of the Gauss--Hermite functions in the hope of replicating this property. In the discrete case, however, no analytical results connecting the chirp rate of the signal to the angle at which we obtain an impulse exist. Defined via the fractional matrix power of the centered version of the DFT, computation of this transform has been constrained due to the need for computing an eigenvalue decomposition. Analysis of the centered version of the DFRFT obtained from Grunbaum\u27s tridiagonal commuter and the kernel associated with it reveals the presence of both amplitude and frequency modulation in contrast to just frequency modulation seen in the continuous case. Furthermore, the instantaneous frequency of the basis functions of the DFRFT are sigmoidal rather than linear. In this report, we define a centered version of the DFRFT based on the Grunbaum commutor and investigate its capabilities towards representing and concentrating chirp signals in a few transform coefficients. We then propose a fast algorithm using the FFT for efficient computation of the multiangle version of the CDFRFT (MA-CDFRFT) using symmetries in the computed eigenvectors to reduce the size of the eigenvalue problem. We further develop approximate empirical relations that will enable us to estimate the chirp rate of the multicomponent chirp signals from the peaks of the computed MA-CDFRFT. This MA-CDFRFT also lays the ground work for a novel chirp rate Vs. frequency signal representation that is more suitable for the time-frequency analysis of multicomponent chirp signals

High Voltage Insulation Surface Condition Analysis Using Time Frequency Distributions

In high voltage engineering, insulation is the most important part to prevent the flow of current to undesired paths. Currently, polymeric type of insulation is widely used because of its advantages which are light, easy to fabricate, and have good dielectric properties compared to traditional ceramic or non polymeric insulation. In previous researches, leakage current frequency component is mainly used to analyze surface condition of polymeric insulation and it is, normally, analyzed by using fast Fourier transform (FFT). However, the technique only presents spectral information and is not suitable for the leakage current signal that consists of magnitude and frequency variations. Thus, time-frequency analysis technique needs to be employed to provide spectral and temporal information of the signal. This research presents the analysis of leakage current using time-frequency distributions (TFDs). Time-frequency distributions (TFDs) such as spectrogram and S-transform are applied to represent the leakage current (LC) in time-frequency representation (TFR). These techniques extract relevant information from TFR include root mean square current (RMS), total harmonic distortion (THD), total non harmonic distortion (TnHD) and total current waveform distortion (TWD). Tracking and erosion test via Incline Plane Test complying with BS EN60587-2007 is conducted to collect different leakage current patterns on polymeric and non polymeric material. Furthermore, the performance of the TFDs is evaluated based on their TFRs accuracy and the results shows that S-transform outperforms spectrogram in term of frequency and time resolution. Thus, the classification of leakage current using parameters from S-transform can be implemented to determine material state and severity instantaneously

Diagnosis of induction motor faults via gabor analysis of the current in transient regime

© 2011 IEEE. Personal use of this material is permitted. Permissíon from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertisíng or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.[EN] Time-frequency analysis of the transient current in induction motors (IMs) is the basis of the transient motor current signature analysis diagnosis method. IM faults can be accurately identified by detecting the characteristic pattern that each type of fault produces in the time-frequency plane during a speed transient. Diverse transforms have been proposed to generate a 2-D time-frequency representation of the current, such as the short time Fourier transform (FT), the wavelet transform, or the Wigner-Ville distribution. However, a fine tuning of their parameters is needed in order to obtain a high-resolution image of the fault in the time-frequency domain, and they also require a much higher processing effort than traditional diagnosis techniques, such as the FT. The new method proposed in this paper addresses both problems using the Gabor analysis of the current via the chirp z-transform, which can be easily adapted to generate high-resolution time-frequency stamps of different types of faults. In this paper, it is used to diagnose broken bars and mixed eccentricity faults of an IM using the current during a startup transient. This new approach is theoretically introduced and experimentally validated with a 1.1-kW commercial motor in faulty and healthy conditions. © 2012 IEEE.This work was supported by the Spanish Ministerio de Ciencia e Innovacion (MICINN) in the framework of the VI Plan Nacional de Investigacion Cientifica, Desarrollo e Innovacion Tecnologica 2008-2011. (Programa Nacional de proyectos de Investigacion Fundamental, project reference DPI2011-23740). The Associate Editor coordinating the review process for this paper was Dr. Subhas Mukhopadhyay.Riera-Guasp, M.; Pineda-Sanchez, M.; Pérez-Cruz, J.; Puche-Panadero, R.; Roger-Folch, J.; Antonino-Daviu, J. (2012). Diagnosis of induction motor faults via gabor analysis of the current in transient regime. IEEE Transactions on Instrumentation and Measurement. 61(6):1583-1596. doi:10.1109/TIM.2012.2186650S1583159661