Time-frequency Approach Research Articles

Enhancement of Classification Accuracy of a Time-frequency Approach for an EEG-based Brain-computer Interface

The aim of this paper is to develop a new algorithm to enhance the performance of EEG-based brain-computer interface (BCI). We improved our time-frequency approach of classification of motor imagery (MI) tasks for BCI applications. The approach consists of Laplacian filtering, band-pass filtering and classification by correlation of time-frequency-spatial patterns. Through off-line analysis of data collected during a "cursor control" experiment, we evaluated the capability of our new method to reveal major features of the EEG control for enhancement of MI classification accuracy. The pilot results in a human subject are promising, with an accuracy rate of 96.1%.

Bearing fault diagnosis using FFT of intrinsic mode functions in Hilbert–Huang transform

A number of techniques for detection of faults in rolling element bearing using frequency domain approach exist today. For analysing non-stationary signals arising out of defective rolling element bearings, use of conventional discrete Fourier transform (DFT) has been known to be less efficient. One of the most suited time–frequency approach, wavelet transform (WT) has inherent problems of large computational time and fixed-scale frequency resolution. In view of such constraints, the Hilbert–Huang Transform (HHT) technique provides multi-resolution in various frequency scales and takes the signal's frequency content and their variation into consideration. HHT analyses the vibration signal using intrinsic mode functions (IMFs), which are extracted using the process of empirical mode decomposition (EMD). However, use of Hilbert transform (HT)-based time domain approach in HHT for analysis of bearing vibration signature leads to scope for subjective error in calculation of characteristic defect frequencies (CDF) of the rolling element bearings. The time resolution significantly affects the calculation of corresponding frequency content of the signal. In the present work, FFT of IMFs from HHT process has been incorporated to utilise efficiency of HT in frequency domain. The comparative analysis presented in this paper indicates the effectiveness of using frequency domain approach in HHT and its efficiency as one of the best-suited techniques for bearing fault diagnosis (BFD).

Time Frequency Characterization of Evoked Brain Activity In Multiple Electrode Recordings

This paper explores global time frequency approaches to EEG data analysis with the Wigner Distribution Function and the Symmetric Ambiguity Function. The task chosen was to characterize the activity profile of EEG signals in sample Frontal, Central and Occipital electrodes from human subjects, coincident with the perception of a reversal in the orientation of a bistable Necker cube figure. The result of this analysis has implications for blind signal processing as the goal was to identify an unknown input source eliciting the observed EEG signals. The methods demonstrate an internally initiated EEG signal source not tied to a regularly anticipated external source. The results demonstrate the general applicability of the methods for a wide variety of neural and biological signals and systems. The findings can be summarized as the observation of high energy activity patterns in terms of significant dissimilarities in the waveform, both in time and frequency, in the Frontal and Occipital electrodes, approximately 200-600 ms prior to the appearance of the premotor potentials in the medial electrodes.

Two-dimensional quantum propagation using wavelets in space and time

A recent method for solving the time-dependent Schrodinger equation has been developed using expansions in compact-support wavelet bases in both space and time [H. Wang et al., J. Chem. Phys. 121, 7647 (2004)]. This method represents an exact quantum mixed time-frequency approach, with special initial temporal wavelets used to solve the initial value problem. The present work is a first extension of the method to multiple spatial dimensions applied to a simple two-dimensional (2D) coupled anharmonic oscillator problem. A wavelet-discretized version of norm preservation for time-independent Hamiltonians discovered in the earlier one-dimensional investigation is verified to hold as well in 2D and, by implication, in higher numbers of spatial dimensions. The wavelet bases are not restricted to rectangular domains, a fact which is exploited here in a 2D adaptive version of the algorithm.

Time-Frequency Analysis of Sjöstrand’s Class

We investigate the properties an exotic symbol class of pseudodifferential operators, Sjöstrand's class, with methods of time-frequency analysis (phase space analysis). Compared to the classical treatment, the time-frequency approach leads to striklingly simple proofs of Sjöstrand's fundamental results and to far-reaching generalizations.

Sensor, Signal and Image Informatics

The number of articles published annually in the fields of biomedical signal and image acquisition and processing is increasing. Based on selected examples, this survey aims at comprehensively demonstrating the recent trends and developments. Four articles are selected for biomedical data acquisition covering topics such as dose saving in CT, C-arm X-ray imaging systems for volume imaging, and the replacement of dose-intensive CT-based diagnostic with harmonic ultrasound imaging. Regarding biomedical signal analysis (BSA), the four selected articles discuss the equivalence of different time-frequency approaches for signal analysis, an application to Cochlea implants, where time-frequency analysis is applied for controlling the replacement system, recent trends for fusion of different modalities, and the role of BSA as part of a brain machine interfaces. To cover the broad spectrum of publications in the field of biomedical image processing, six papers are focused. Important topics are content-based image retrieval in medical applications, automatic classification of tongue photographs from traditional Chinese medicine, brain perfusion analysis in single photon emission computed tomography (SPECT), model-based visualization of vascular trees, and virtual surgery, where enhanced visualization and haptic feedback techniques are combined with a sphere-filled model of the organ. The selected papers emphasize the five fields forming the chain of biomedical data processing: (1) data acquisition, (2) data reconstruction and pre-processing, (3) data handling, (4) data analysis, and (5) data visualization. Fields 1 and 2 form the sensor informatics, while fields 2 to 5 form signal or image informatics with respect to the nature of the data considered. Biomedical data acquisition and pre-processing, as well as data handling, analysis and visualization aims at providing reliable tools for decision support that improve the quality of health care. Comprehensive evaluation of the processing methods and their reliable integration in routine applications are future challenges in the field of sensor, signal and image informatics.

Detecting time-dependent coherence between non-stationary electrophysiological signals—A combined statistical and time–frequency approach

Various time–frequency methods have been used to study time-varying properties of non-stationary neurophysiological signals. In the present study, a time–frequency coherence estimate using continuous wavelet transform (CWT) together with its confidence intervals are proposed to evaluate the correlation between two non-stationary processes. The approach is based on averaging over repeat trials. A systematic comparison between approaches using CWT and short-time Fourier transform (STFT) is carried out. Simulated data are generated to test the performance of these methods when estimating time–frequency based coherence. In contrast to some recent studies, we find that CWT based coherence estimates do not supersede STFT based estimates. We suggest that a combination of STFT and CWT would be most suitable for analysing non-stationary neural data. Tests are presented to investigate the time and frequency discrimination capabilities of the two approaches. The methods are applied to two experimental data sets: electroencephalogram (EEG) and surface electromyogram (EMG) during wrist movements in a healthy subject, and local field potential (LFP) and surface EMG recordings during resting tremor in a Parkinsonian patient. Supporting software is available at http://www.dcs.warwick.ac.ukffeng/software/COD and http://www.neurospec.org.

Wheel-flat diagnostic tool via wavelet transform

The detection and acknowledgement of signatures, for condition monitoring and fault diagnostics by wavelet transform, deserves increased attention, due to its property of variable time–frequency resolution, which overcomes limitations of classical time–frequency approaches. In the paper, a diagnostic tool is presented, based on the wavelet transform, able to detect and to quantify the wheel-flat defect of a test train at different speeds and to measure the train speed with proper accuracy. The designed diagnostic tool minimises the hardware requirements, since only one accelerometer is needed, and provides results in real time. The results, achieved by an exhaustive experimental campaign, permit to validate the effectiveness of the diagnostic tool and to demonstrate the advantages of wavelet-based detection of signatures.

Rail inspection in track maintenance: A benchmark between the wavelet approach and the more conventional Fourier analysis

Nowadays the power of data analysis tools like the wavelet decomposition of signals is well known and spread. On the other hand the theoretical advantages of such methods often fight with reality, when real field signals are collected and analysed: it sometimes comes out that this time–frequency approach somehow fails, demanding for a deeper insight into the kind of physical problem to be considered, and requiring a sort of “benchmark” between the traditional Fourier approach and the more recent time–frequency one. In this paper, sharply application-oriented, the possibilities offered by the wavelet techniques have been analysed: both the DSP specialist and the field engineer points of view have been joined to exploit the new approach of its best. A real problem has been considered, in which acceleration signals from a train bogie are collected and real-time analysed, to get a diagnostic tool to know the track condition of a subway line. This paper would like to look for a compromise point between complex mathematics based techniques, such as wavelet packet, sometimes hard to comprehend to the application engineer, and the physical meaning of these tools helping in fixing the real method limits. Therefore the aim is not just trying this analysis on an almost random process, like the accelerations measured on a running bogie, to locate defects, but rather a discussion on the development of the continuous and discrete wavelet transform, in comparison with the classical Fourier analysis or filter banks. Only the minimum mathematical background is provided in the text, with the needed references, to give tools fit for comprehending the physical meaning of the new tools, capable of sparing computing effort, while preserving or even improving the system effectiveness.

Individual Time-Dependent Spectral Boundaries for Improved Accuracy in Time-Frequency Analysis of Heart Rate Variability

Heart rate variability (HRV) is a major noninvasive technique for evaluating the autonomic nervous system (ANS). Use of time-frequency approach to analyze HRV allows investigating the ANS behavior from the power integrals, as a function of time, in both steady-state and non steady-state. Power integrals are examined mainly in the low-frequency and the high-frequency bands. Traditionally, constant boundaries are chosen to determine the frequency bands of interest. However, these ranges are individual, and can be strongly affected by physiologic conditions (body position, breathing frequency). In order to determine the dynamic boundaries of the frequency bands more accurately, especially during autonomic challenges, we developed an algorithm for the detection of individual time-dependent spectral boundaries (ITSB). The ITSB was tested on recordings from a series of standard autonomic maneuvers with rest periods between them, and the response to stand was compared to the known physiological response. A major advantage of the ITSB is the ability to reliably define the mid-frequency range, which provides the potential to investigate the physiologic importance of this range.

A Time-Frequency Approach to Feature Extraction for a Brain-Computer Interface with a Comparative Analysis of Performance Measures

The paper presents an investigation into a time-frequency (TF) method for extracting features from the electroencephalogram (EEG) recorded from subjects performing imagination of left- and right-hand movements. The feature extraction procedure (FEP) extracts frequency domain information to form features whilst time-frequency resolution is attained by localising the fast Fourier transformations (FFTs) of the signals to specific windows localised in time. All features are extracted at the rate of the signal sampling interval from a main feature extraction (FE) window through which all data passes. Subject-specific frequency bands are selected for optimal feature extraction and intraclass variations are reduced by smoothing the spectra for each signal by an interpolation (IP) process. The TF features are classified using linear discriminant analysis (LDA). The FE window has potential advantages for the FEP to be applied in an online brain-computer interface (BCI). The approach achieves good performance when quantified by classification accuracy (CA) rate, information transfer (IT) rate, and mutual information (MI). The information that these performance measures provide about a BCI system is analysed and the importance of this is demonstrated through the results.

A time-frequency approach to the adjustable bandwidth concept

Abstract The aim of the adjustable bandwidth concept (ABC) is to enhance nonstationary signals in noise by bringing out the main features so that they be effectively used in detection and classification algorithms. We show that the method transforms a time-frequency distribution by means of individual time-frequency transformations into a set of final time-frequency distributions. Each step of the procedure can be understood and formulated in terms of the kernel method. Explicit expressions are derived and examples are given. The formulation suggests further enhancements of the method.

Multigroup classification of audio signals using time-frequency parameters

The ongoing advancements in the multimedia technologies drive the need for efficient classification of the audio signals to make the content-based retrieval process more accurate and much easier from huge databases. The challenge of this task lies in an accurate extraction of signal characteristics so as to derive a strong discriminatory feature suitable for classification. In this paper, a time-frequency (TF) approach for audio classification is proposed. Audio signals are nonstationary in nature and TF approach is the best way to analyze them. The audio signals were decomposed using an adaptive TF decomposition algorithm, and the signal decomposition parameter based on octave (scaling) was used to generate a set of 42 features over three frequency bands within the auditory range. These features were analyzed using linear discriminant functions and classified into six music groups (rock, classical, country, jazz, folk and pop). Overall classification accuracies as high as 97.6 % was achieved by linear discriminant analysis of 170 audio signals.

Wick calculus : A time-frequency approach

The purpose of this paper is to present a formula for the product of two Wick operators, defined in terms of different pairs of windows φ1, φ2. In principle, Wick operators can be converted to Weyl operators, and hence one may apply to them the standard symbolic calculus [14, 21]. It is natural, however, to consider the product in the Wick form, and try to compute directly the symbol in terms of the symbols of the factors; see in this direction [3, 5, 15, 16, 19]. Recently Ando and Morimoto [1] have given a full expansion for the Wick symbol of the product in the case when all the windows coincide with the Gaussian function. We propose here a general formula. The expression is somewhat non-standard, because we write the product as a sum of anti-Wick operators corresponding to a sequence of different pairs of windows, with decreasing order. This seems to us the only possible expression of reasonable simplicity in the generic case. In the remaining part of this Introduction we recall the definition of Wick operators and state the composition result. In Section 2 we summarize some concepts of time-frequency methods used in the proof. In Section 3 we introduce the classes of symbols we are arguing on. They are, essentially, those of Shubin [18], as generalized in [3]. Let us emphasize that other classes of symbols, under weaker assumptions on derivative estimates, would work as well. In Section 4 we prove the result. In Section 5 we give a composition formula for the particular case of Gaussian functions as a pair of windows and we recapture the results of Lerner [15, 16], Ando and Morimoto [1]. Section 6 is devoted to miscellaneous comments. Namely we show how to pass from a pair of windows to another and, finally, we construct a parametrix for the elliptic Wick operators by using our formula; a natural application, which we hope to detail in future papers, concerns regularity results in the frame of the modulation spaces [9, 12]. Before stating the precise definition, let us observe that Wick operators have been considered in the past under rather different points of view, and different names. They were introduced by Berezin [2] as a quantization procedure, and as an approximation of pseudodifferential operators (“wave packets”) by Cordoba and Fefferman [7, 11]. From the point of view of the time-frequency analysis, which we shall adopt in the following, they have been studied by Daubechies [8] and

Discrimination of Pathological Voices Using a Time-Frequency Approach

Acoustical measures of vocal function are routinely used in the assessments of disordered voice, and for monitoring the patient's progress over the course of voice therapy. Typically, acoustic measures are extracted from sustained vowel stimuli where short-term and long-term perturbations in fundamental frequency and intensity, and the level of "glottal noise" are used to characterize the vocal function. However, acoustic measures extracted from continuous speech samples may well be required for accurate prediction of abnormal voice quality that is relevant to the client's "real world" experience. In contrast with sustained vowel research, there is relatively sparse literature on the effectiveness of acoustic measures extracted from continuous speech samples. This is partially due to the challenge of segmenting the speech signal into voiced, unvoiced, and silence periods before features can be extracted for vocal function characterization. In this paper we propose a joint time-frequency approach for classifying pathological voices using continuous speech signals that obviates the need for such segmentation. The speech signals were decomposed using an adaptive time-frequency transform algorithm, and several features such as the octave max, octave mean, energy ratio, length ratio, and frequency ratio were extracted from the decomposition parameters and analyzed using statistical pattern classification techniques. Experiments with a database consisting of continuous speech samples from 51 normal and 161 pathological talkers yielded a classification accuracy of 93.4%.

Forced vibration behaviour and crack detection of cracked beams using instantaneous frequency

In this paper, a new method for crack detection in beams based on instantaneous frequency and empirical mode decomposition is proposed. The dynamic behaviour of a cantilever beam with a breathing crack under harmonic excitation is investigated both theoretically and experimentally. A simple single-degree-of-freedom system with varying stiffness is employed to simulate the dynamic behaviour of the beam. The time-varying stiffness is modelled using a simple periodic function. Both simulated and experimental response data are analysed by applying empirical mode decomposition and Hilbert transform and the instantaneous frequency of each oscillatory mode is obtained. It is shown that the instantaneous frequency oscillates between frequencies corresponding to the open and closed states revealing the breathing of the crack. The variation of the instantaneous frequency increases with increasing crack depth following a polynomial law and consequently can be used for estimation of crack size. Using the intrinsic modes of the system, the harmonic distortion of the distorted sinusoidal response is calculated. It follows that the harmonic distortion increases with crack depth following definite trends and can be also used as an effective indicator for crack size. The proposed time–frequency approach is superior compared to Fourier analysis and can be used to improve the effectiveness of vibration-based crack detection techniques.

Implementations of Shannon’s sampling theorem, a time-frequency approach

Implementations of Shannon’s sampling theorem, a time-frequency approach

Cochlear maturation and otoacoustic emissions in preterm infants: a time–frequency approach

Click-evoked otoacoustic emissions (CEOAEs) from preterm infants were analyzed to characterize developmental changes of cochlear active mechanisms. Due to their strong time-varying properties, CEOAEs were studied with a time–frequency approach – the wavelet transform (WT). By means of the WT, CEOAEs were decomposed into 12 frequency bands, spanning the 0.25–6.25 kHz range. For each band, the root-mean-square (RMS) level and latency were studied as functions of both frequency and age. Because CEOAEs were averaged using the non-linear mode of acquisition, the developmental changes in observed in this study are related to the non-linear component (which is actually the most predominant component of the active cochlear response) of CEOAEs, the linear one being mostly canceled out by non-linear averaging. In our study, there was evidence that properties of CEOAE non-linear components are related to the post-conception age (PCA) in that the levels and latency of CEOAE frequency components changed until the age of about 38 weeks post-conception, whereas after 38 weeks, CEOAE features were very similar to those of term newborns. In particular, the CEOAE levels increased and latency decreased with age. The observed changes in CEOAE properties seem to reveal a development of cochlear active mechanisms, although contributions from outer and middle ear development cannot be excluded. Also, in agreement with previous physiological and behavioral findings, our results revealed that the development of CEOAE properties was not the same for all the frequencies, being greater for frequencies ⩽4 kHz, and resembled the development of the cochlear partition, which proceeds from base to apex.

Combination Method of Principal Component and Wavelet Analysis for Multivariate Process Monitoring and Fault Diagnosis

Product quality and operation safety are important aspects of industrial processes, particularly those with large numbers of correlated process variables. Principal component analysis (PCA) has been widely used in multivariate process monitoring for its ability to reduce process dimensions. PCA and other statistical techniques, however, have difficulties in differentiating faults with similar time-domain process characteristics. A wavelet-based time-frequency approach is developed in this paper to improve PCA-based methods by extending the time-domain process features into time-frequency information. Subsequently, a similarity measure is presented to compare process features for on-line process monitoring and fault diagnosis. Simulation results show that the proposed multivariate time-frequency process feature is effective in both fault detection and diagnosis, illustrating the potentials for real-world application.

A neuro-genetic and time-frequency approach to macromodeling dynamic hysteresis in the harmonic regime

A numerical approach for the evaluation of hysteresis loops in the harmonic regime is presented. Genetic algorithms (GAs) are used to train neural networks (NNs) with the aim of generalizing the Jiles-Atherton (JA) static hysteresis model for dynamic loops. The NN training is based on symmetrical and asymmetrical, major and minor loops under sinusoidal excitation with or without offset. Subsequently, the harmonic magnetic time period has been partitioned into suitable time windows into which the field has been fitted by sinusoids with offset. New JA parameters, estimated by the trained NNs in each partitioning time window, have been inserted into the JA static model to calculate the magnetization waveform, time window by time window. Validations are shown.