Showing papers on "Time–frequency analysis published in 2009"

Higher-Order Properties of Analytic Wavelets

Abstract: The influence of higher-order wavelet properties on the analytic wavelet transform behavior is investigated, and wavelet functions offering advantageous performance are identified. This is accomplished through detailed investigation of the generalized Morse wavelets, a two-parameter family of exactly analytic continuous wavelets. The degree of time/frequency localization, the existence of a mapping between scale and frequency, and the bias involved in estimating properties of modulated oscillatory signals, are proposed as important considerations. Wavelet behavior is found to be strongly impacted by the degree of asymmetry of the wavelet in both the frequency and the time domain, as quantified by the third central moments. A particular subset of the generalized Morse wavelets, recognized as deriving from an inhomogeneous Airy function, emerge as having particularly desirable properties. These ldquoAiry waveletsrdquo substantially outperform the only approximately analytic Morlet wavelets for high time localization. Special cases of the generalized Morse wavelets are examined, revealing a broad range of behaviors which can be matched to the characteristics of a signal.

Output only modal identification and structural damage detection using time frequency & wavelet techniques

Abstract: The primary objective of this paper is to develop output only modal identification and structural damage detection. Identification of multi-degree of freedom (MDOF) linear time invariant (LTI) and linear time variant (LTV—due to damage) systems based on Time-frequency (TF) techniques—such as short-time Fourier transform (STFT), empirical mode decomposition (EMD), and wavelets—is proposed. STFT, EMD, and wavelet methods developed to date are reviewed in detail. In addition a Hilbert transform (HT) approach to determine frequency and damping is also presented. In this paper, STFT, EMD, HT and wavelet techniques are developed for decomposition of free vibration response of MDOF systems into their modal components. Once the modal components are obtained, each one is processed using Hilbert transform to obtain the modal frequency and damping ratios. In addition, the ratio of modal components at different degrees of freedom facilitate determination of mode shape. In cases with output only modal identification using ambient/random response, the random decrement technique is used to obtain free vibration response. The advantage of TF techniques is that they are signal based; hence, can be used for output only modal identification. A three degree of freedom 1:10 scale model test structure is used to validate the proposed output only modal identification techniques based on STFT, EMD, HT, wavelets. Both measured free vibration and forced vibration (white noise) response are considered. The secondary objective of this paper is to show the relative ease with which the TF techniques can be used for modal identification and their potential for real world applications where output only identification is essential. Recorded ambient vibration data processed using techniques such as the random decrement technique can be used to obtain the free vibration response, so that further processing using TF based modal identification can be performed.

The robustness of seismic attenuation measurements using fixed- and variable-window time-frequency transforms

Abstract: Frequency-based methods for measuring seismic attenuation are used commonly in exploration geophysics. To measure the spectrum of a nonstationary seismic signal, different methods are available, including transforms with time windows that are either fixed or systematically varying with the frequency being analyzed. We compare four time-frequency transforms and show that the choice of a fixed- or variable-window transform affects the robustness and accuracy of the resulting attenuation measurements. For fixed-window transforms, we use the short-time Fourier transform and Gabor transform. The S-transform and continuous wavelet transform are analyzed as the variable-length transforms. First we conduct a synthetic transmission experiment, and compare the frequency-dependent scattering attenuation to the theoretically predicted values. From this procedure, we find that variable-window transforms reduce the uncertainty and biasof the resulting attenuation estimate, specifically at the upper and lower ends of th...

Time--frequency analysis of biosignals

Abstract: The wavelet transform has a powerful time-frequency analysis and signal-coding tool suitable for use in the manipulation of complex nonstationary signals. This article provides an overview of the emerging role of wavelet-transform analysis in biomedical signal processing and analysis. It also provides a brief overview of the theory of the transform in its two distinct and very different forms: continuous and discrete. In conclusion, it has been shown that the wavelet transform is a flexible time-frequency decomposition tool that can form the basis of useful signal analysis, and coding schemes. It is envisaged that the future will see further application of the wavelet transform to biomedical signal analysis, as the emerging technologies based on them are honed for practical purposes.

Time-frequency analysis of fourier integral operators

Abstract: Time-frequency methods are used to study a class of Fourier Integral Operators (FIOs) whose representation using Gabor frames is proved to be very efficient. Indeed, similarly to the case of shearlets and curvelets frames [10, 35], the matrix representation of a Fourier Integral Operator with respect to a Gabor frame is well-organized. This is used as a powerful tool to study the boundedness of FIOs on modulation spaces. As special cases, we recapture boundedness results on modulation spaces for pseudo-differential operators with symbols in $M^{\infty, 1}$ [33], for some Fourier multipliers [6] and metaplectic operators [14, 31]. Moreover, this paper provides the mathematical tools to numerically solving the Cauchy problem for Schr¨odinger equations using Gabor frames [17]. Finally, similar arguments can be employed to study other classes of FIOs [16].

Detection of leak acoustic signal in buried gas pipe based on the time―frequency analysis

Abstract: A time–frequency technique for locating leaks in buried gas distribution pipes involves the use of the cross-correlation on two measured acoustic signals on either side of a leak. This technique can be problematic for locating leaks in steel pipes, as the acoustic signals in these pipes are generally narrow-band and low frequency. The effectiveness of the time–frequency technique for detecting leaks in steel pipes was investigated experimentally in an earlier study. The object of this paper is to identify the characteristics of this dispersive acoustic wave through analysis of the cut-off frequency by using the time–frequency method experimentally and BEM (boundary element method) theoretically for the development of an experimental tool to analyze the leak signals in steel pipe. The tool is based on experimental work and theoretical formulation of wave propagation in a fluid-filled pipe. This tool uses the time–frequency method to explain some of the features of wave propagation measurements made in gas pipes. Leak noise signals are generally passed through a time–frequency filter for detection of impulse signal related leakage.

Deconvolutive Short-Time Fourier Transform Spectrogram

Abstract: The short-time Fourier transform (STFT) spectrogram, which is the squared modulus of the STFT, is a smoothed version of the Wigner-Ville distribution (WVD). The STFT spectrogram is 2-D convolution of the the signal WVD and the window function WVD. In this letter, we propose a deconvolutive short-time Fourier transform (DSTFT) spectrogram method, which improves the time-frequency resolution and reduces the cross-terms simultaneously by applying a 2-D deconvolution operation on the STFT spectrogram. Compared to the STFT spectrogram, the spectrogram obtained by the proposed method shows a clear improvement in the time-frequency resolution. Computer simulations are provided to illustrate the good performance of the proposed method, compared with some traditional time-frequency representation (TFR) methods.

Three uncertainty relations for real signals associated with linear canonical transform

Abstract: Uncertainty principle plays an important role in signal processing, physics and mathematics, and it represents the relations between time spread and frequency spread (or position and velocity). Linear canonical transform (LCT) is one generalisation of Fresnel transform, fractional Fourier transform and others. The LCT has been used in physical optics and signal processing. Three novel results of uncertainty principle in the LCT domains are obtained here, in which one is connected with parameters a and b and the other one is connected with c and d; the last one is connected with the four transformation parameters a, b, c and d. Their physical meanings are given as well. These results disclose the inequalities' relations between two spreads, between two group delays and between one spread and one group delay in the LCT domains. It also shows that any one of the three cases can reduce to classical uncertainty principle in time/frequency domain. The effects of time scaling on these results' bounds are also involved.

Time-Delay Estimation of Chirp Signals in the Fractional Fourier Domain

Abstract: A new time-delay estimator is presented in this paper. It is evaluated based on the delay property of the fractional Fourier transform with less computation and is suitable for chirp signals. The statistical analysis in terms of signal-to-noise ratio (SNR) and estimation accuracy for this estimation is also studied. The proposed method for the time delay yields a variance which is theoretically equal to the Cramer-Rao lower bound. The validity of this estimation method is demonstrated via simulations.

The nonlinear and nonstationary properties in EEG signals: Probing the complex fluctuations by Hilbert-huang transform

Abstract: The analysis of biological fluctuations provides an excellent route to probe the underlying mechanisms in maintaining internal homeostasis of the body, especially under the challenges of the ever-changing environment or disease processes. However, the features of nonlinearity and nonstationarity in physiological time series limit the reliability of the conventional analysis. Hilbert–Huang transform (HHT), based on nonlinear theory, is an innovative approach to extract the dynamic information at different time scales, in particular, from nonstationary signals. In this paper, HHT is introduced to analyze the alpha waves of human's electroencephalography (EEG), which seemly oscillate regularly between 8 and 12 Hz in healthy subject but getting irregular or disappeared in different demented status. Furthermore, conventional time–frequency analyses are adopted to collate the results from those methods and HHT. Finally, the potential usages of HHT are demonstrated in characterizing the biological signals qualitatively and quantitatively, including stationarity analysis, instantaneous frequency and amplitude modulation or correlation analysis. Such applications on EEG have successively disclosed the differences of alpha rhythms between normal and demented brains and the nonlinear characteristics of the underlying mechanisms. Hopefully, in addition to empower the studies of EEG varied in diseased, aging, and physiological processes, these methods might find other applications in EEG analysis.

An Improved S-Transform for Time-Frequency Analysis

Abstract: The time-frequency representation (TFR) has been used as a powerful technique to identify, measure and process the time varying nature of signals. In the recent past S-transform gained a lot of interest in time-frequency localization due to its superiority over all the existing identical methods. It produces the progressive resolution of the wavelet transform maintaining a direct link to the Fourier transform. The S-transform has an advantage in that it provides multi resolution analysis while retaining the absolute phase of each frequency component of the signal. But it suffers from poor energy concentration in the time-frequency domain. It gives degradation in time resolution at lower frequency and poor frequency resolution at higher frequency. In this paper we propose a modified Gaussian window which scales with the frequency in a efficient manner to provide improved energy concentration of the S-transform. The potentiality of the proposed method is analyzed using a variety of test signals. The results of the study reveal that the proposed scheme can resolve the time-frequency localization in a better way than the standard S-transform.

Compressive image sampling with side information

Abstract: Compressive sampling is a novel framework that exploits sparsity of a signal in a transform domain to perform sampling below the Nyquist rate. In this paper, we apply compressive sampling to reduce the sampling rate of images/video. The key idea is to exploit the intra- and inter-frame correlation to improve signal recovery algorithms. The image is split into non-overlapping blocks of fixed size, which are independently compressively sampled exploiting sparsity of natural scenes in the Discrete Cosine Transform (DCT) domain. At the decoder, each block is recovered using useful information extracted from the recovery of a neighboring block. In the case of video, a previous frame is used to help recovery of consecutive frames. The iterative algorithm for signal recovery with side information that extends the standard orthogonal matching pursuit (OMP) algorithm is employed. Simulation results are given for Magnetic Resonance Imaging (MRI) and video sequences to illustrate advantages of the proposed solution compared to the case when side information is not used.

Low frequency shadow detection of gas reservoirs in time-frequency domain

Abstract: In order to depict the local fine structure of seismic signal,implement instantaneous spectral decomposition of 3D seismic data with high computational efficiency and detect low frequency shadow related to gas reservoirs,a generalized S transform(GST)was presented in the paper.GST alters the fixed wavelet basis of existing S transform by introducing two parameters.The wavelet basis of GST is adjustable in accordance with the real application.The results in the simulation of signal model demonstrate that GST is more adaptive with more excellent time-frequency localization.The mechanism of low frequency shadow is introduced here.GST is applied in instantaneous spectral decomposition of real 3D seismic data.The method can not only detect low frequency shadow but also indicate the lithologic edge and spatial distribution of gas reservoirs,which decreases the uncertainty in gas reservoirs detection.

A new perspective for the IEEE standard 1459-2000 via stationary wavelet transform in the presence of nonstationary power quality disturbance

Abstract: Power components, power factors and pollution factor are defined according to the IEEE Std. 1459-2000 based on the FFT. However, the FFT in the presence of nonstationary Power Quality (PQ) disturbances results in inaccurate values due to its sensitivity to the spectral leakage problem. In this paper, a new perspective for the IEEE Std. 1459-2000 definitions is introduced using the Stationary Wavelet Transform (SWT). As a time-frequency transform, SWT can provide variable frequency resolution while preserving time information with no spectral leakage as the FFT. Moreover, unlike other time-frequency transform such as Discrete Wavelet Transform (DWT), SWT possess the time-invariance property that keeps the time and frequency characteristics throughout all the decomposition levels. Results of different case studies including stationary, nonstationary of synthetic and real PQ disturbances proves the effectiveness of applying the SWT over FFT or DWT.

Adaptive Nonlinear System Identification in the Short-Time Fourier Transform Domain

Abstract: In this paper, we introduce an adaptive algorithm for nonlinear system identification in the short-time Fourier transform (STFT) domain. The adaptive scheme consists of a parallel combination of a linear component, represented by crossband filters between subbands, and a quadratic component, which is modeled by multiplicative cross-terms. We adaptively update the model parameters using the least-mean-square (LMS) algorithm, and derive explicit expressions for the transient and steady-state mean-square error (MSE) in frequency bins for white Gaussian inputs. We show that estimation of the nonlinear component improves the MSE performance only when the power ratio of nonlinear to linear components is relatively high. Furthermore, as the number of crossband filters increases, a lower steady-state MSE may be obtained at the expense of slower convergence. Experimental results support the theoretical derivations.

Time–Frequency Phase Analysis of Ictal EEG Recordings With the S-Transform

Abstract: The calculation and visualization of temporal and phase information in the brain, such as during cognitive processes and epileptiform activity, is an important tool in EEG-based studies of physiological brain activation. To this end, we present a technique that estimates the phase and time offsets between different channels in EEG recordings of seizure activity. The offset information is visually combined with amplitude information to emphasize the most significant signal features. The estimates of phase and time offset are derived from the S-transform, a time-frequency representation that is similar to a windowed Fourier transform, but with a wavelet-like, scalable window. The phase offsets are obtained from the differences between phase spectra of S-transforms of different traces, and the time offsets are then obtained from the frequency-domain gradients of the phase offsets. This is analogous to the link between frequency ldquophase rampingrdquo and time translation in ordinary Fourier analysis. In this paper, we present a synthetic example to help describe the method, and then show Ictal EEG recordings from two human subjects. The differences between the recording times of spike-wave discharges at different electrodes exhibit behavior that is strongly dependent on time and frequency.

Recursive Time-Frequency Reassignment

Abstract: A fast algorithm for creating time-frequency representations based on a special case of the short-time Fourier transform (STFT) is presented. The algorithm is extended with the method known as time-frequency reassignment. This approach makes time-frequency reassignment well suited for real-time implementations.

The Detection of Frequency Hopping Signal Using Compressive Sensing

Abstract: 1 hyajia@126.com; 2 tpw0802@163.com Abstract: Compressive sensing (CS) creates a new framework of signal reconstruction or approximation from a smaller set of incoherent projection compared with the traditional Nyquist-rate sampling theory. Re- cently, it has been shown that CS can solve some signal processing problems given incoherent measurements without ever reconstructing the signals. Moreover, the number of measurements necessary for most compres- sive signal processing application such as detection, estimation and classification is lower than that necessary for signal reconstruction. Based on CS, this paper presents a novel identification algorithm of frequency hop- ping (FH) signals. Given the hop interval, the FH signals can be identified and the hopping frequencies can be estimated with a tiny number of measurements. Simulation results demonstrate that the method is effective and efficient.

Stationarization via surrogates

Abstract: The surrogate data method, classically used for non-linearity tests, amounts to the use of some constrained noise providing a reference for statistical testing. It is revisited here as a method for stationarization and this feature is put forward in the context of non-stationarity testing. The stationarization property of surrogates is first explored in a time–frequency perspective and used for devising a test of stationarity relative to an observation time. Then, more general forms of surrogates are developed, directly in time–frequency or mixed domains of representation (ambiguity and time-lag domains included), and it is shown how they allow for other tests of non-stationary features: detection of the existence of a transient in some noise; assessment of non-stationary cross-correlations.

Noise components identification in biomedical signals based on Empirical Mode Decomposition

Abstract: Hilbert-Huang Transform (HHT) is composed of the Empirical Mode Decomposition (EMD) as the first step of the procedure and Hilbert Spectral analysis (HSA) as the second step. It is a recent tool in the analysis of signals originating from nonlinear processes as well as nonstationary signals. Empirical Mode Decomposition produces a set of Intrinsic Mode Functions and the core idea is based on the assumption that any data consists of different simple intrinsic modes of oscillations. Statistical significance of the Intrinsic Mode Functions and partial signal reconstruction are investigated in this paper. Application of Hilbert-Huang Transform on biomedical signals such as ECG from MIT-BIH database and experimental respiratory signals acquired by means of accelerometers, reveal the adaptive nature of the method.

Bearing fault detection and diagnosis based on teager–huang transform

Abstract: A new approach to fault diagnosis of bearings based on the Teager–Huang Transform (THT) is presented. This method is based on the Empirical Mode Decomposition (EMD) and Teager Kaiser Energy Operator (TKEO) techniques. EMD can adaptively decompose the vibration signal into a series of zero mean Amplitude Modulation-Frequency Modulation (AM-FM) Intrinsic Mode Functions (IMFs). TKEO can track the instantaneous amplitude and instantaneous frequency of the AM-FM component at any instant. The experimental examples are conducted to evaluate the effectiveness of the proposed approach. The experimental results provide strong evidence that the performance of the Teager–Huang Transform approach is better than that of the Hilbert–Huang Transform approach for bearing fault detection. The Teager–Huang Transform has better resolution than the Hilbert–Huang Transform. The Teager–Huang Transform can effectively diagnose the faults of the bearing, thus providing a viable processing tool for gearbox defect monitoring.

Instantaneous spectral attributes using scales in continuous-wavelet transform

Abstract: Instantaneous spectral properties of seismic data — center frequency, root-mean-square frequency, bandwidth — often are extracted from time-frequency spectra to describe frequency-dependent rock properties. These attributes are derived using definitions from probability theory. A time-frequency spectrum can be obtained from approaches such as short-time Fourier transform (STFT) or time-frequency continuous-wavelet transform (TFCWT). TFCWT does not require preselecting a time window, which is essential in STFT. The TFCWT method converts a scalogram (i.e., time-scale map) obtained from the continuous-wavelet transform (CWT) into a time-frequency map. However, our method includes mathematical formulas that compute the instantaneous spectral attributes from the scalogram (similar to those computed from the TFCWT), avoiding conversion into a time-frequency spectrum. Computation does not require a predefined window length because it is based on the CWT. This technique optimally decomposes a multiscale signal. F...

A Digital Implementation of Flickermeter in the Hybrid Time and Frequency Domains

Abstract: Voltage fluctuations caused by rapidly changing loads in the power systems may give rise to noticeable illumination flickers of lighting equipment. The voltage flickers can also cause malfunctions in many electric devices. This paper presents a digital implementation of flickermeter in the hybrid time and frequency domains based on IEC standard 61000-4-15. In addition, this paper proposes a new demodulation method to extract the voltage envelope. Simulations and actual measurements show that the digital implementation with the proposed method yields relatively accurate flicker measurements.

A class of highly concentrated time-frequency distributions based on the ambiguity domain representation and complex-lag moment

Abstract: A class of time-frequency distributions with complex-lag argument is proposed. It is based on the ambiguity domain representations of real and complex-lag moment, combined to provide a cross-terms free representation for multicomponent signals. Furthermore, the distributions from the proposed class provide a more effective instantaneous frequency estimation for signals with fast varying phase function than the existing approach. The theory is illustrated by the examples.