Time-frequency Analysis Of Signals Research Articles

Time–frequency filtering of MEG signals with matching pursuit

Time–frequency signal analysis based on various decomposition techniques is widely used in biomedical applications. Matching Pursuit is a new adaptive approach for time–frequency decomposition of such biomedical signals. Its advantage is that it creates a concise signal approximation with the help of a small set of Gabor atoms chosen iteratively from a large and redundant set. In this paper, the usage of Matching Pursuit for time–frequency filtering of biomagnetic signals is proposed. The technique was validated on artificial signals and its performance was tested for varying signal-to-noise ratios using both simulated and real MEG somatic evoked magnetic field data.

A Review on Time-frequency, Time-scale and Scale-frequency Domain Signal Analysis

This paper presents a review on Time-frequency, Time-scale and Scale-frequency domain signal analysis. The distinctive features of these techniques are discussed with respect to the decomposition of a signal at different resolutions. The concept of “Time-frequency”, “Time-scale” and “Scale-frequency” analysis of a signal has been explained. Some examples are presented to reveal the suitability of these techniques. The main thrust is to focus the use of these techniques for different digital signal and image processing applications.

A generalized demodulation approach to time-frequency projections for multicomponent signals

In this paper, we introduce a flexible approach for the time-frequency analysis of multicomponent signals involving the use of analytic vectors and demodulation. The demodulated analytic signal is projected onto the time-frequency plane so that, as closely as possible, each component contributes exclusively to a different ‘tile’ in a wavelet packet tiling of the time-frequency plane, and at each time instant, the contribution to each tile definitely comes from no more than one component. A single reverse demodulation is then applied to all projected components. The resulting instantaneous frequency of each component in each tile is not constrained to a set polynomial form in time, and is readily calculated, as is the corresponding Hilbert energy spectrum. Two examples illustrate the method. In order better to understand the effect of additive noise, the approximate variance of the estimated instantaneous frequency in any tile has been formulated by starting with pure noise and studying its evolving covariance structure through each step of the algorithm. The validity and practical utility of the resulting expression for the variance of the estimated instantaneous frequency is demonstrated via a simulation experiment.

Orthonormal-Basis Partitioning and Time-Frequency Representation of Cardiac Rhythm Dynamics

Although a number of time-frequency representations have been proposed for the estimation of time-dependent spectra, the time-frequency analysis of multicomponent physiological signals, such as beat-to-beat variations of cardiac rhythm or heart rate variability (HRV), is difficult. We thus propose a simple method for 1) detecting both abrupt and slow changes in the structure of the HRV signal, 2) segmenting the nonstationary signal into the less nonstationary portions, and 3) exposing characteristic patterns of the changes in the time-frequency plane. The method, referred to as orthonormal-basis partitioning and time-frequency representation (OPTR), is validated using simulated signals and actual HRV data. Here we show that OPTR can be applied to long multicomponent ambulatory signals to obtain the signal representation along with its time-varying spectrum.

New aggressive way to search for the best base in wavelet packets

The binary-tree best base (BTBB) searching method developed by Coifman and Wickerhauser is well known and widely used in wavelet packet applications. However, the requirement that the base vectors be chosen from either a parent or its directly related children in the binary-tree structure is a limitation because it does not search all possible orthogonal bases and therefore may not provide an optimal result. We have recently found that the set of all possible orthogonal bases in a wavelet packet is much larger than the set searched by the BTBB method. Based on this observation, we have developed a Tree-elimination based Best orthogonal Base (TBB) searching method: a new way to search the best base among a much larger set of orthogonal bases. In this paper, we show that considerable improvements in signal compression, time-frequency analysis, and feature extraction may be achieved using the newly developed TBB method. Similar to the matching pursuit method, TBB uses an aggressive searching method. However, its computation is faster than that of the orthogonal matching pursuit (MP) searching method.

Erratum to: Time-Frequency Analysis of Electronystagmogram Signals in Patients with Congenital Nystagmus

Erratum to: Time-Frequency Analysis of Electronystagmogram Signals in Patients with Congenital Nystagmus

A Nonlinear Time-Frequency Analysis Method

An alternative method of time-frequency signal analysis is introduced and is compared with the conventional discrete Fourier transfer (DFT)-based methods. The structure of the proposed algorithm and its mathematical properties are presented. The proposed algorithm has a nonlinear structure that provides a frequency-adaptivity feature. It can be implemented both in analog and in digital form and is particularly suitable for real-time applications where computational efficiency is important. A comparison is made with the DFT in terms of algorithm efficiency, sensitivity, and complexity. It is shown that compared with the DFT, the algorithm is more efficient for real-time applications and is less sensitive to noise and variations in the frequency and sampling rate while maintaining simplicity of the structure and computational efficiency. Slower convergence rate of the algorithm, compared with the DFT, constitutes its main shortcoming.

Time-frequency analysis of electronystagmogram signals in patients with congenital nystagmus.

To evaluate the usefulness of the short-time Fourier transform (STFT) in the analysis of temporal congenital nystagmus characteristics. We carried out an observational case series in patients with congenital nystagmus. An electronystagmogram (ENG) recording was performed for 300 s in 13 consecutive subjects with congenital nystagmus (age: 7-68 years). Digitized ENG signals (12 bits, 100 Hz) were divided into 2-s segments with a Hanning window, and a Fourier transform was carried out for each segment. The power spectrum obtained for each segment was graphically reconstructed as a function of time. The results were compared among the patients. Clear periodicity in the time-frequency distribution was observed in 3 of the 13 patients (23%). One of the three patients was diagnosed with periodic alternating nystagmus, but the other two patients showed periodicity without alternation of beat direction. No significant difference was observed in clinical characteristics, except for sex, between patients who showed periodicity and those who did not. Some patients with congenital nystagmus showed clear periodicity in the nystagmus waveform without alternation of beat direction. The STFT is a useful tool to evaluate the temporal characteristics of congenital nystagmus in clinics.

The Bargmann analytic representation in signal analysis

The Bargmann analytic representation of quantum mechanics is used in the context of time–frequency signal analysis. Transformations between the various representations are derived. Examples that show how this method can be implemented numerically and demonstrate its robustness to noise are discussed.

Detection of land-mines using ultra-wideband radar data and time–frequency signal analysis

The authors present a study of the backscattered signatures from various types of land-mines placed either on the Earth's surface or buried underground, and their time–frequency (t–ν) distributions. A BoomSAR designed by the Army Research Laboratory (ARL) transmits ultra-wideband (UWB) signals to a test area to be inspected. The backscattered signals are used to form synthetic aperture radar (SAR) imagery and also the corresponding time–frequency distributions. The t–ν plots are generated of the distributions of several mines and ‘confusers’ (i.e. undesirable debris that are similar to mines in terms of amplitude and shape). For both metal and plastic mines, SAR images are generated and the t–ν distributions are obtained using the backscattered signals generated by an electromagnetic (EM) numerical model and are compared against the measured data. Time–frequency characteristics of mines and confusers that may be useful for demining purposes are investigated. Although measurements and EM predictions show good agreement in most cases, the main purpose of the work is to obtain the characteristics of the t–ν distributions of the actual (dielectric and conducting) mines used, as well as those of the ‘confusers’ so that they can be distinguished from the true mines. This has been achieved in all cases shown, and many distinctive features of each have been identified. These could later be used for the development of automated algorithms for in-situ mine detection and could be combined with alternative approaches that have also shown promise for classification purposes, as planned for future research.

Wavelet based robust sub-band features for phoneme recognition

Wavelet transform has been found to be an effective tool for the time-frequency analysis of non-stationary and quasi-stationary signals. Recent years have seen wavelet transform being used for feature extraction in speech recognition applications. In the paper a sub-band feature extraction technique based on an admissible wavelet transform is proposed and the features are modified to make them robust to additive white Gaussian noise. The performance of this system is compared with the conventional mel frequency cepstral coefficients (MFCC) under various signal to noise ratios. The recognition performance based on the eight sub-band features is found to be superior under the noisy conditions compared with MFCC features.

Automatic Decomposition of Wigner Distribution and its Application to Heart Rate Variability

We introduce an algorithm for the automatic decomposition of Wigner Distribution (WD) and we applied it for the quantitative extraction of Heart Rate Variability (HRV) spectral parameters during non-stationary events. Early response to tilt was investigated. Quantitative analysis of multi-components non-stationary signals is obtained through an automatic decomposition of WD based on least square (LS) fitting of the instantaneous autocorrelation function (ACF). Through this approach the different signal and interference terms which contributes to the ACF may be separated and their parameters (instantaneous frequency and amplitude) quantified. A beat-to-beat monitoring of HRV spectral components is obtained. Analysis of simulated signals demonstrated the capability of the proposed approach to track and separate the signal components. Analysis of HRV data evidenced different dynamics in the early Autonomic Nervous System (ANS) response to tilt. The novel approach to the quantification of the beat-to-beat HRV spectral parameters obtained from decomposition of Wigner distribution was demonstrated to be effective in the analysis of HRV data. Relevant physiological information about the dynamics of the early sympathetic response to tilt were obtained. The method is a general approach which may be employed for a quantitative time-frequency analysis of non-stationary biological signals.

Time-Frequency Analysis of Brain Electrical Activity – Adaptive Approximations

We present an approach to time-frequency analysis of bioelectrical signals. The method relays on the decomposition of the signal into a set of waveforms that have good localization both in time and in frequency. The waveforms belong to a highly redundant set of functions - allowing for a very accurate description of signal components. Properties of the method are illustrated by simulations and applications to EEG. The presented method delivers a common formalism suitable for describing both gross statistical properties of structures present in bioelectrical signals, as well as microstructure of chosen phenomena.

Time–frequency signal analysis based on the windowed fractional Fourier transform

A new signal-adaptive joint time–frequency distribution for the analysis of nonstationary signals is proposed. It is based on a fractional-Fourier-domain realization of the weighted Wigner distribution producing auto-terms close to the ones in the Wigner distribution itself, but with reduced cross-terms. Improvement over the standard time–frequency representations is achieved when the principal axes of a signal (defined as mutually orthogonal directions in the time–frequency plane for which the width of the signal's fractional power spectrum is minimum or maximum) do not correspond to time and frequency. The computational cost of this fractional-domain realization is the same as the computational cost of the realizations in the time or the frequency domain, since the windowed Fourier transform of the fractional Fourier transform of a signal corresponds to the short-time Fourier transform of the signal itself, with the window being the fractional Fourier transform of the initial one. The appropriate fractional domain is found from the knowledge of three second-order fractional Fourier transform moments. Numerical simulations confirm a qualitative advantage in the time–frequency representation, when the calculation is done in the optimal fractional domain. The approach can be generalized to the time–frequency distributions from the Cohen class.

Time‐Frequency Signal Analysis of Earthquake Records Using Mexican Hat Wavelets

Abstract: A method is presented for time‐frequency signal analysis of earthquake records using Mexican hat wavelets. Ground motions in earthquakes are postulated as a sequence of simple penny‐shaped ruptures at different locations along a fault line and occurring at different times. The single point source displacement of ground motion is idealized by a Gaussian function. For the purpose of signal analysis of accelerograms, the ground motion record generated by a simple penny‐shaped rupture is used to form the basis wavelet function. After a careful study of the characteristics of various wavelet functions, the Mexican hat wavelet was found to be the most appropriate wavelet basis function to represent the acceleration of a single point source rupture. The result of the signal processing of an accelerogram is presented in the form of a scalogram using the coefficients of the continuous Mexican hat wavelet transform to describe the signal energy in the time‐scale domain. The proposed signal processing methodology can be used to investigate the characteristics of accelerograms recorded on various types of sites and their effects on different types of structures.

New Evaluation Method on Gear Dynamics Using Continuous and Discrete Wavelet Transforms

The aim of this study is to propose a new evaluation method of gear dynamics using the continuous and discrete wavelet transforms. The wavelet transform (WT) is a method for the time-frequency analysis of signals. In order to evaluate the difference in the gear dynamics due to the gear materials, which are sintered and steel ones, the dynamic characteristics of gears were measured using a power circulating gear testing machine. The gear dynamics were analyzed in a time-frequency domain by the continuous and discrete WTs. The new evaluation method using the WTs proposed in this paper was more useful compared with the conventional one to investigate the damping characteristic and the dynamic condition of the gear equipment.

Resolution measure criteria for the objective assessment of the performance of quadratic time-frequency distributions

This paper presents the essential elements for developing objective methods of assessment of the performance of time-frequency signal analysis techniques. We define a measure for assessing the resolution performance of time-frequency distributions (TFDs) in separating closely spaced components in the time-frequency domain. The measure takes into account key attributes of TFDs, such as components mainlobes and sidelobes and cross-terms. The introduction of this measure allows to quantify the quality of TFDs instead of relying solely on visual inspection of their plots. The method of assessment of performance of TFDs also allows the improvement of methodologies for designing high-resolution quadratic TFDs for time-frequency analysis of multicomponent signals. Different TFDs, including the modified B distribution, are optimized using this methodology. Examples of a performance comparison of quadratic TFDs in resolving closely spaced components in the time-frequency domain, using the proposed resolution measure, are provided.

Evaluation Method of Gear Dynamic Performance Using Information in Time-Frequency Domain.

The wavelet transform (WT) is a method for the time-frequency analysis of signals. It is possible to detect the change in each frequency through a sampling period by the WT. In this study, in order to discuss an evaluation method for the gear dynamic performance using the time-frequency analysis, the dynamic performance of both sintered and steel gears were measured using a power circulating gear testing machine in the range of the rotational speeds of 1600 to 10000 rpm. The measured signals of dynamic performance, which are tooth root strain, vibration and sound of gear box, were analyzed in the time-frequency domain by the continuous WT based on the Gabor function, and the signals of the dynamic performance were decomposed and reconstructed by the discrete WT based on the cardinal B-spline function. The validity on the new evaluation method using both continuous and discrete WTs was discussed. The dynamic performance can be divided between two frequency regions over and under the tooth mesh frequency fz. Consequently, it was clarified that the dynamic performance over the fz indicated the condition of the torsional vibration of gear system, and the dynamic performance under fz depended on the rotational speed of gear.

Wavelet energy spectrum for time‐frequency localization of earthquake energy

AbstractThe authors recently developed a method for time‐frequency signal analysis of earthquake records using Mexican hat wavelets. Ground motions in earthquakes are postulated as a sequence of simple penny‐shaped ruptures at different locations along a fault line and occurring at different times. In this article, a wavelet energy spectrum is proposed for time‐frequency localization of the earthquake input energy. The ground acceleration generated by a simple penny‐shaped rupture is used as the basis to form the mother wavelet. The symmetric Mexican hat wavelet is chosen as the mother wavelet. The spectrum is presented pictorially in a two‐dimensional, time‐frequency domain. The proposed wavelet energy spectrum can be used to observe the evolution of the frequency contents of earthquake energy over time and distance of the site from the epicenter in a more accurate manner than the traditional time series (accelerogram) or frequency domain (Fourier amplitude spectrum) representation. It can be viewed as a microscope for looking into the time‐frequency characteristics of earthquake acceleration records. The wavelet energy spectrum provides frequency evolution information to be used in the structural design process. © 2003 Wiley Periodicals, Inc. Int J Imaging Syst Technol 13, 133–140, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ima.10038

Suppression of narrow-band interference in DS-spread spectrum systems using adaptive IIR notch filter

This paper proposes an algorithm for the suppression of narrow-band interference in direct sequence spread spectrum systems, based on the open-loop adaptive IIR notch filtering. In the open-loop notch filtering schemes, it is assumed that the frequency and power estimates are given or obtained by time-frequency analysis of input signal. In this paper, we estimate the frequency and power of the interference by using the adaptive lattice IIR notch filter. Another lattice IIR notch filter of the same structure is placed in front of the receiver, the notch of which is controlled by the frequency estimate in order to remove the interference. However, since the conventional IIR notch filters have zeros constrained on the unit circle, they also remove the information signal at the notch frequency while removing the interference at the same time. Hence, we adjust the depth of the notch with respect to the interference power, for the trade-off between data distortion and interference reduction. The objective function for adjusting the depth of the notch is defined as the overall signal to noise ratio (SNR). The SNR is expressed as a function of filter parameters, and the notch depth that maximizes the SNR is found. Simulation results show that the proposed algorithm yields comparable or better performance than the open-loop FIR notch filter, conventional FIR LMS, and nonlinear adaptive filters with long taps.