An optimally concentrated Gabor transform for localized time-frequency components

Gabor analysis is one of the most common instances of time-frequency signal analysis. Choosing a suitable window for the Gabor transform of a signal is often a challenge for practical applications, in particular in audio signal processing. Many time-frequency (TF) patterns of different shapes may be present in a signal and they can not all be sparsely represented in the same spectrogram. We propose several algorithms, which provide optimal windows for a user-selected TF pattern with respect to different concentration criteria. We base our optimization algorithm on $l^p$-norms as measure of TF spreading. For a given number of sampling points in the TF plane we also propose optimal lattices to be used with the obtained windows. We illustrate the potentiality of the method on selected numerical examples

Adaptive filtering techniques for gravitational wave interferometric data: Removing long-term sinusoidal disturbances and oscillatory transients

It is known by the experience gained from the gravitational wave detector proto-types that the interferometric output signal will be corrupted by a significant amount of non-Gaussian noise, large part of it being essentially composed of long-term sinusoids with slowly varying envelope (such as violin resonances in the suspensions, or main power harmonics) and short-term ringdown noise (which may emanate from servo control systems, electronics in a non-linear state, etc.). Since non-Gaussian noise components make the detection and estimation of the gravitational wave signature more difficult, a denoising algorithm based on adaptive filtering techniques (LMS methods) is proposed to separate and extract them from the stationary and Gaussian background noise. The strength of the method is that it does not require any precise model on the observed data: the signals are distinguished on the basis of their autocorrelation time. We believe that the robustness and simplicity of this method make it useful for data preparation and for the understanding of the first interferometric data. We present the detailed structure of the algorithm and its application to both simulated data and real data from the LIGO 40meter proto-type.Comment: 16 pages, 9 figures, submitted to Phys. Rev.

A note on reassigned Gabor spectrograms of Hermite functions

An explicit form is given for the reassigned Gabor spectrogram of an Hermite function of arbitrary order. It is shown that the energy concentration sharply localizes outside the border of a clearance area limited by the ''classical'' circle where the Gabor spectrogram attains its maximum value, with a perfect localization that can only be achieved in the limit of infinite order

Designing Gabor windows using convex optimization

Redundant Gabor frames admit an infinite number of dual frames, yet only the canonical dual Gabor system, constructed from the minimal l2-norm dual window, is widely used. This window function however, might lack desirable properties, e.g. good time-frequency concentration, small support or smoothness. We employ convex optimization methods to design dual windows satisfying the Wexler-Raz equations and optimizing various constraints. Numerical experiments suggest that alternate dual windows with considerably improved features can be found

A Fast Signal-Dependent Time-Frequency Representation

In last few years, in order to overcome same limitations of the short time Fourier transform (STFT), while avoiding the cross-terms that make the Wigner distribution difficult to interpret, some signal-dependent time-frequency representations (SDTFR) have been proposed. In this paper, the authors introduce a computationally efficient signal-dependent time-frequency method which is suitable for on-line analysis. This SDTFR uses a Gaussian window (GW) similar to STFT, but varies the parameter σ of the GW with time to achieve high signal concentration and high resolution in time. The parameter σ can be automatically calculated by the slope of instantaneous frequency (IF) and instantaneous bandwidth (IB) at that time.published_or_final_versio

A Critical Review of Time-frequency Distribution Analysis for Detection and Classification of Harmonic Signal in Power Distribution System

This paper presents a critical review of time-frequency distributions (TFDs) analysis for detection and classification of harmonic signal. 100 unique harmonic signals comprise of numerous characteristic are detected and classified by using spectrogram, Gabor transform and S-transform. The rulebased classifier and the threshold settings of the analysis are according to the IEEE Standard 1159 2009. The best TFD for harmonic signals detection and classification is selected through performance analysis with regards to the accuracy, computational complexity and memory size that been used during the analysis