Reduced Interference Distribution Research Articles

Parallel LSTM-CNN Network With Radar Multispectrogram for Human Activity Recognition

Owing to the ability of automatic feature extraction, deep learning is extensively applied in human activity recognition (HAR) based on radar. In this article, a recognition method based on a multispectrogram and deep-learning model is proposed. The radar echo data are transformed into spectrograms with different feature expressions by performing three time–frequency analyses, including short-time Fourier transform (STFT), reduced interference distribution with Hanning kernel (RIDHK), and smoothed pseudo-Wigner–Ville distribution (SPWVD), and then the spectrograms are sent to deep-learning model to realize HAR. The model employs three long short-term memory (LSTM) networks to learn the temporal features of the spectrograms and uses a 3-D convolutional neural network (3-DCNN) to extract the independent spatial features of a single spectrogram and the spatial correlation features between different kinds of spectrograms, named parallel LSTM-CNN network (PLCN). The PLCN is capable of effectively improving the degree of feature utilization in the spectrogram and the accuracy of human activity classification by fusing both temporal and spatial features. The final experimental results show that the average recognition accuracy of the method based on the PLCN for eight human activities reaches 94.75%, which is significantly higher than that of the three parallel LSTMs and the single 3-DCNN.

Human Activity Recognition Based on Mixed CNN With Radar Multi-Spectrogram

Deep learning makes radar-based human activity recognition (HAR) attract more attention in the fields of intelligent security, traffic management, medical rehabilitation and military operation, because it has the ability to automatically extract comprehensive features of human activity. This paper proposes a recognition method based on multi-spectrogram and mixed convolutional neural network (MCNN). Specifically, three time-frequency analyses, including short-time Fourier transform (STFT), reduced interference distribution with Hanning kernel (RIDHK) and smoothed pseudo Wigner-Ville distribution (SPWVD), are performed on radar echo data to obtain the time-frequency spectrograms with different feature expressions, and then the spectrograms are fed into the MCNN for recognition and classification. In the MCNN, three two-dimensional CNNs (2DCNNs) are used to extract the independent spatial features from three types of spectrograms, and one three-dimensional CNN (3DCNN) with unit convolution kernel is employed to focus on extracting the correlation features between three kinds of spectrograms. The behavioral features in the spectrograms are characterized comprehensively by fusing these two kinds of features, which is able to improve the recognition accuracy. Experimental results illustrate that the proposed method improves the average recognition accuracy of eight human activities by at least 2.16% compared with other methods.

Rayleigh damping parameters estimation using hammer impact tests

Structural Health Monitoring (SHM) systems for aerospace applications are becoming more prevalent and its potential cost-benefit relation is rapidly improving as more structures that were traditionally made with metallic materials are gradually being replaced by composites. To support these systems, simulations can play a crucial role; however, in the case of low energy impacts, the structural damping becomes a very significant element in the simulation. This damping is usually not well known, or is based in estimates with very low reliability. Therefore, in order to improve the reliability of these values this paper presents an attempt to estimate the Rayleigh damping parameters with the application of time-frequency analysis methods to transient signals, specifically, the reduced interference distribution. These parameters are estimated based in the results of a large number of structural tests done in a square carbon-fiber reinforced plastic panel, and are then validated by correlation of an explicit Finite Element Method (FEM) simulation. A discussion on how to apply the reduced interference distribution to the signals measured by piezoelectric sensors under an impact scenario and other possible usages of these results is also presented in this document.

Time-Frequency Based Phase-Amplitude Coupling Measure For Neuronal Oscillations

Oscillatory activity in the brain has been associated with a wide variety of cognitive processes including decision making, feedback processing, and working memory. The high temporal resolution provided by electroencephalography (EEG) enables the study of variation of oscillatory power and coupling across time. Various forms of neural synchrony across frequency bands have been suggested as the mechanism underlying neural binding. Recently, a considerable amount of work has focused on phase-amplitude coupling (PAC)– a form of cross-frequency coupling where the amplitude of a high frequency signal is modulated by the phase of low frequency oscillations. The existing methods for assessing PAC have some limitations including limited frequency resolution and sensitivity to noise, data length and sampling rate due to the inherent dependence on bandpass filtering. In this paper, we propose a new time-frequency based PAC (t-f PAC) measure that can address these issues. The proposed method relies on a complex time-frequency distribution, known as the Reduced Interference Distribution (RID)-Rihaczek distribution, to estimate both the phase and the envelope of low and high frequency oscillations, respectively. As such, it does not rely on bandpass filtering and possesses some of the desirable properties of time-frequency distributions such as high frequency resolution. The proposed technique is first evaluated for simulated data and then applied to an EEG speeded reaction task dataset. The results illustrate that the proposed time-frequency based PAC is more robust to varying signal parameters and provides a more accurate measure of coupling strength.

Reduced Interference Vertex-Frequency Distributions

Vertex-frequency analysis of graph signals is a challenging topic for research and applications. Counterparts of the short-time Fourier transform, the wavelet transform, and the Rihaczek distribution have recently been introduced to the graph-signal analysis. In this letter, we have extended the energy distributions to a general reduced interference distributions class. It can improve the vertex-frequency representation of a graph signal while preserving the marginal properties. This class is related to the spectrogram of graph signals as well. Efficiency of the proposed representations is illustrated in examples.

Design and Properties of a Family of Reduced Interference Distributions

A family of Doppler-lag kernels is introduced to design the reduced interference distributions. The proposed kernel functions with two parameters \({{\varvec{n}}}\) and \({\varvec{\alpha }}\) are of the product \({\varvec{\nu }} {\varvec{\tau }} \) and satisfy all the nine desirable kernel constraints. The family of Cohen time–frequency distributions with these kernels includes some existing reduced interference distributions such as Margenau–Hill, Born–Jordan and Bessel distributions. Also the signal-to-interference ratio (SIR) in time–frequency plane is defined, and reduced interference capabilities with \({{\varvec{n}}}\) and \({\varvec{\alpha }}\) are discussed. Simulations show that the greater the \({{\varvec{n}}}\) and \({\varvec{\alpha }}\) are, the greater the SIR.

Time-frequency phase-synchrony approaches with ERPs

Time-frequency signal processing approaches are well-developed, and have been widely employed for the study of the energy distribution of event-related potential (ERP) data across time and frequency. Wavelet time-frequency transform (TFT) and Cohen's class of time-frequency distributions (TFD) are the most widely used in the field. While ERP TFT approaches have been most extensively developed for amplitude measures, reflecting the magnitude of regional neuronal activity, time-frequency phase-synchrony measures have gained increased utility in recent years for the assessment of functional connectivity. Phase synchrony measures can be used to index the functional integration between regions (interregional), in addition to the consistency of activity within region (intertrial). In this paper, we focus on a particular class of time-frequency distributions belonging to Cohen's class, known as the Reduced Interference Distribution (RID) for quantifying functional connectivity, which we recently introduced (Aviyente et al., 2011). The present report first summarizes common time-frequency approaches to computing phase-synchrony with ERP data in order to highlight the similarities and differences relative to the RID. In previous work, we demonstrated differences between the RID and wavelet approaches to indexing phase-synchrony, and have applied the RID to demonstrate that RID-based time-frequency phase-synchrony measures can index increased functional connectivity between medial and lateral prefrontal regions during control processing, observed in the theta band during the error-related negativity (ERN). Because ERN amplitude measures have been associated with two other widely studied medial-frontal theta components (no-go N2; feedback negativity, FN), the application of the RID phase synchrony measure in the present report extends our previous work with ERN to include theta activity during the no-go N2 (inhibitory processing) and the feedback negativity (FN; loss feedback processing). Findings support the idea that similar medial-lateral prefrontal functional connectivity underlies the ERN, no-go N2, and FN components, and provide initial validation that the proposed RID-based time-frequency phase-synchrony measure can index this activity.

Using a time-frequency distribution to identify buried channels in reflection seismic data

Geological events such as thin beds and channels cannot be easily revealed on seismic sections due to the interference of reflections from the top and bottom of the layer. Buried channel is one of the hydrocarbon traps, which is important in oil and gas exploration. Spectral decomposition can be used to indicate subtle changes in channel thickness. In using the Fourier transform only the frequency content of the changes is displayed; hence, the exact onset of the changes is missed. Time-frequency distributions are suitable approaches to display and interpret information embedded in non-stationary signals such as seismic signals. Spectral decomposition can be used for seismic attributes calculation, which is used for imaging of thin beds. The conventional spectral decompositions such as Short Time Fourier Transform (STFT) and Wigner–Ville Distribution (WVD) have limitations in terms of Heisenberg uncertainty principle and cross-terms artefacts, respectively. In this paper, we used the Reduced Interference Distribution (RID) for buried channel identification to overcome the mentioned limitations. We compared the obtained results of RID with those of Smoothed Pseudo WVD. The real seismic data is selected from one of the western oil fields of Iran. Our results indicate that a better resolution is achieved by RID in both vertical and lateral stratigraphic features.

Signal segmentation using changing regression models with application in seismic engineering

The change detection and segmentation methods have gained considerable attention in scientific research and appear to be the central issue in various application areas. The objective of the paper is to present a segmentation method, based on maximum a posteriori probability (MAP) estimator, with application in seismic signal processing; some interpretations and connections with other approaches in change detection and segmentation, as well as computational aspects in this field are also discussed. The experimental results obtained by Monte Carlo simulations for signal segmentation using different signal models, including models with changes in the mean, in FIR, AR and ARX model parameters, as well as comparisons with other methods, are presented and the effectiveness of the proposed approach is proved. Finally, we discuss an application of segmentation in the analysis of the earthquake records during the Kocaeli seism, Turkey, August 1999, Arcelik station (ARC). The optimal segmentation results are compared with time–frequency analysis, for the reduced interference distribution (RID). The analysis results confirm the efficiency of the segmentation approach used, the change instants resulted by MAP appearing clear in energy and frequency contents of time–frequency distribution.

A harmonic vibration, output only and time-frequency representation based method for damage detection in Concrete piers of complex bridges

Due to damage, vibrations of bridge piers compared with undamaged state would be changed. A new signal-based algorithm is proposed to extract feature and detect damage in complex bridges. According to the proposed algorithm, it is necessary to vibrate the bridge before and after damage by exciting force and record responses at the middle and top of the piers. For this purpose, sine and cosine transient forces were applied to the analytical model of Ghotour Bridge and the signals of pier responses were recorded. Using reduced interference distribution, the response signals were processed and time-frequency plans were calculated. Modified matrix subtraction method was proposed to detect damage. Based on the results, damage was identified and located with good accuracy. The proposed algorithm is an output-only method and in practice there is no need to create an analytical model of an existing complex bridge for damage detection.

Using Reduced Interference Distribution to Analyze Abnormal Cardiac Signal

Using Reduced Interference Distribution to Analyze Abnormal Cardiac SignalDue to the non-stationary, multicomponent nature of biomedical signals, the use of time-frequency analysis can be inevitable for these signals. The choice and selection of the proper Time-Frequency Distribution (TFD) that can reveal the exact multicomponent structure of biological signals is vital in many applications, including the diagnosis of medical abnormalities. In this paper, the instantaneous frequency techniques using two distribution functions are applied for analysis of biological signals. These distributions are the Wigner-Ville Distribution and the Bessel Distribution. The simulation performed on normaland abnormal cardiac signals show that the Bessel Distribution can clearly detect the QRS complexes. However, Wigner-Ville Distribution was able to detect the QRS complexes in the normal signa, but fails to detect these complexes in the abnormal cardiac signal.

Time–frequency analysis of movement-related spectral power in EEG during repetitive movements: A comparison of methods

During dynamic voluntary movements, power in the α- and β-bands resulting from synchronized neuronal activity is modulated in a manner that is time-locked to movement onset. These signals can be readily recorded from the scalp surface using electroencephalography. Abnormalities in the magnitude and timing of these oscillations are present in a wide variety of movement disorders including Parkinson's disease and dystonia. Most studies have examined movement-related oscillations in the context of single discrete movements, yet marked impairments are often seen during the performance of repetitive movements. For this reason, there is considerable need for analysis methods that can resolve the modulation of these oscillations in both the frequency and time domains. Presently, there is little consensus on which is the most appropriate method for this purpose. In this paper, a comparison of commonly used time–frequency methods is presented for the analysis of movement-related power in the α- and β-bands during repetitive movements. The same principles hold, however, for any form of repetitive or rhythmic input–output processes in the brain. In particular, methods based on band-pass filtering, the short-time Fourier transform (STFT), continuous wavelet transform and reduced interference distributions are discussed. The relative merits and limitations in terms of spectral or temporal resolution of each method are shown with the use of simulated and experimental data. It is shown that the STFT provides the best compromise between spectral and temporal resolution and thus is the most appropriate approach for the analysis and interpretation of repetitive movement-related oscillations in health and disease.

Time-frequency analysis and modeling of the backscatter of categorized dolphin echolocation clicks for target discrimination

A set of dolphin echolocation clicks collected from an Atlantic bottlenose dolphin in Kaneohe Bay, Hawai'i from a previous experiment is examined in terms of their time and frequency characteristics. The center frequency and rms bandwidth are calculated for the clicks and these are clustered into four classes by using a model based on the Bayesian information criterion. The echo signatures are attained from a solid, elastic homogeneous sphere for each class of clicks from an acoustic scattering model. The results from the scattering model are compared to experimental values. The joint time-frequency content of the resulting echo signals is obtained by the reduced interference distribution (RID). The RIDs are plotted and examined for each signal class for four spherical targets of different material compositions. RID correlation values are obtained for a standard target versus comparison targets by using a time-frequency correlator. The results suggest that dolphins may discriminate by auditory inspection of the time-frequency information returned by the targets. The modification of the outgoing clicks and examination of time-frequency target information may be fundamental to a dolphin's ability to identify and discriminate targets.

Decomposing ERP time–frequency energy using PCA

Objective Time–frequency transforms (TFTs) offer rich representations of event-related potential (ERP) activity, and thus add complexity. Data reduction techniques for TFTs have been slow to develop beyond time analysis of detail functions from wavelet transforms. Cohen's class of TFTs based on the reduced interference distribution (RID) offer some benefits over wavelet TFTs, but do not offer the simplicity of detail functions from wavelet decomposition. The objective of the current approach is a data reduction method to extract succinct and meaningful events from both RID and wavelet TFTs. Methods A general energy-based principal components analysis (PCA) approach to reducing TFTs is detailed. TFT surfaces are first restructured into vectors, recasting the data as a two-dimensional matrix amenable to PCA. PCA decomposition is performed on the two-dimensional matrix, and surfaces are then reconstructed. The PCA decomposition method is conducted with RID and Morlet wavelet TFTs, as well as with PCA for time and frequency domains separately. Results Three simulated datasets were decomposed. These included Gabor logons and chirped signals. All simulated events were appropriately extracted from the TFTs using both wavelet and RID TFTs. Varying levels of noise were then added to the simulated data, as well as a simulated condition difference. The PCA-TFT method, particularly when used with RID TFTs, appropriately extracted the components and detected condition differences for signals where time or frequency domain analysis alone failed. Response-locked ERP data from a reaction time experiment was also decomposed. Meaningful components representing distinct neurophysiological activity were extracted from the ERP TFT data, including the error-related negativity (ERN). Conclusions Effective TFT data reduction was achieved. Activity that overlapped in time, frequency, and topography were effectively separated and extracted. Methodological issues involved in the application of PCA to TFTs are detailed, and directions for further development are discussed. Significance The reported decomposition method represents a natural but significant extension of PCA into the TFT domain from the time and frequency domains alone. Evaluation of many aspects of this extension could now be conducted, using the PCA-TFT decomposition as a basis.

Motion parameters estimation by new propagation approach and time–frequency representations

Estimation of time-varying motion parameters of moving objects is considered. The motion parameters are mapped into the instantaneous frequency (IF) of a frequency modulated signal. The IF estimation is obtained by using the Wigner distribution. Generalization in the case of multiple objects and reduced interference distributions is given. A new propagation approach is proposed for joint estimation of velocity and position of objects in a video-sequence. This approach produces better accuracy than the variable μ -propagation-based one.

Performance of quadratic time~frequency distributions as instantaneous frequency estimators

General performance analysis of the shift covariant class of quadratic time-frequency distributions (TFDs) as instantaneous frequency (IF) estimators, for an arbitrary frequency-modulated (FM) signal, is presented. Expressions for the estimation bias and variance are derived. This class of distributions behaves as an unbiased estimator in the case of monocomponent signals with a linear IF. However, when the IF is not a linear function of time, then the estimate is biased. Cases of white stationary and white nonstationary additive noises are considered. The well-known results for the Wigner distribution (WD) and linear FM signal, and the spectrogram of signals whose IF may be considered as a constant within the lag window, are presented as special cases. In addition, we have derived the variance expression for the spectrogram of a linear FM signal that is quite simple but highly signal dependent. This signal is considered in the cases of other commonly used distributions, such as the Born-Jordan and the Choi-Williams distributions. It has been shown that the reduced interference distributions outperform the WD but only in the case when the IF is constant or its variations are small. Analysis is extended to the IF estimation of signal components in the case of multicomponent signals. All theoretical results are statistically confirmed.

Performance of time-frequency representation techniques to measure blood flow turbulence with pulsed-wave Doppler ultrasound

The current processing performed by commercial instruments to obtain the time-frequency representation (TFR) of pulsed-wave Doppler signals may not be adequate to characterize turbulent flow motions. The assessment of the intensity of turbulence is of high clinical importance and measuring high-frequency (small-scale) flow motions, using Doppler ultrasound (US), is a difficult problem that has been studied very little. The objective was to optimize the performance of the spectrogram (SPEC), autoregressive modeling (AR), Choi–Williams distribution (CWD), Choi–Williams reduced interference distribution (CW-RID), Bessel distribution (BD), and matching pursuit method (MP) for mean velocity waveform estimation and turbulence detection. The intensity of turbulence was measured from the fluctuations of the Doppler mean velocity obtained from a simulation model under pulsatile flow. The Kolmogorov spectrum, which is used to determine the frequency of the fluctuations and, thus, the scale of the turbulent motions, was also computed for each method. The best set of parameters for each TFR method was determined by minimizing the error of the absolute frequency fluctuations and Kolmogorov spectral bandwidth measured from the simulated and computed Doppler spectra. The results showed that different parameters must be used for each method to minimize the velocity variance of the estimator, to optimize the detection of the turbulent frequency fluctuations, and to estimate the Kolmogorov spectrum. To minimize the variance and to measure the absolute turbulent frequency fluctuations, four methods provided similar results: SPEC (10-ms sine-cosine windows), AR (10-ms rectangular windows, model order = 8), CWD (wN and wM = 10-ms rectangular windows, σ = 0.01), and BD (wN = 10-ms rectangular windows, α = 16). The velocity variance in the absence of turbulence was on the order of 0.04 m/s (coefficient of variation ranging from 8.0% to 14.5%, depending on the method). With these spectral techniques, the peak of the turbulence intensity was adequately estimated (velocity bias < 0.01 m/s). To track the frequency of turbulence, the best method was BD (wN = 2-ms rectangular windows, α = 2). The bias in the estimate of the −10 dB bandwidth of the Kolmogorov spectrum was 354 ± 51 Hz in the absence of turbulence (the true bandwidth should be 0 Hz), and −193 ± 371 Hz with turbulence (the simulated −10-dB bandwidth was estimated at 1256 Hz instead of 1449 Hz). In conclusion, several TFR methods can be used to measure the magnitude of the turbulent fluctuations. To track eddies ranging from large vortex to small turbulent fluctuations (wide Kolmogorov spectrum), the Bessel distribution with appropriate set of parameters is recommended. (E-mail: cloutig@ircm.qc.ca)

HELICOPTER TRANSMISSION FAULT DETECTION VIA TIME-FREQUENCY, SCALE AND SPECTRAL METHODS

The vast majority of the powerful and effective algorithms in signal processing start with the assumption of stationarity. In addition, the deterministic portion of the signal is often assumed to be composed of complex exponentials which are the solutions to linear time-invariant (LTI) differential equations. Many signals do not comply with these assumptions, however, resulting in disappointment when conventional techniques are used. We now have at hand time–frequency (t–f) and scale transform analyses which can provide new insights into the nature of non-stationary signals. This paper describes some results using reduced interference distributions (RIDs) and scale transforms in the analysis of signals obtained from accelerometers placed strategically on a Westland helicopter transmission. Fault detection algorithms for several types of faults were compared and the methods based on the scale transform performed best followed by RID results. More conventional spectral-analysis-based methods were the least effective.

Scaled window decompositions for reduced interference time–frequency distributions

The reduced interference distribution (RID) is a time–frequency distribution (and a member of Cohen’s class) which enjoys a number of desirable properties. A simple design procedure, which allows one to start with a simple primitive function, h(t) is provided. When h(t) is equipped with certain constraints, a full RID kernel within Cohen’s class can easily be constructed. RID computation has traditionally been achieved by the ‘‘outer-product methods,’’ wherein the kernel is convolved with the local autocorrelation of the signal along time for each lag value. Amin, Cunningham, and Williams and others have provided alternative methodologies; the ‘‘inner-product methods.’’ This involves decomposition of the kernel into an orthonormal set of windows. Each window is used to form an STFT. We have found that a truncated set of windows can be used to closely approximate RIDs. Wavelet and scale-related windows can be used to generate a discrete time–frequency distribution that closely approximates RIDs. Illustrations of the contributions of each of the windows will be provided. This method of decomposition of the RID leads to new insights into the nature of time–frequency distributions as well as providing a method for very fast computation.

Reduced interference distribution application and interpretation for transient acoustic events

Transient acoustic events often present difficulties when using conventional time-series or spectral methods. The Reduced Interference Distribution (RID) and its derivatives have been under development [W. J Williams and J. Jeong, Time-Frequency Signal Analysis, edited by B. Boashash (Longman Cheshire, New York, 1992)] for several years. The RID was specifically motivated by the need for a better analysis tool for transient acoustic events [ONR Grants N00014-90-J-1654, N00014-97-1-0072]. The deficiencies of the spectrogram for marine mammal sound analysis were early recognized [William Watkins, Marine Bioacoustics 2, 15–43 (1966)]. Watkins’ illustrations of spectrogram deficiencies and updated results obtained using the Wigner distribution (WD) and the RID will be presented. The RID represents an attempt to retain the desirable mathematical properties of the WD while reducing the often troublesome WD interference terms. Examples drawn from several acoustic transients such as marine mammal sounds, joint clicks and vortex formations in turbulent air flow will be used to illustrate the usefulness of the RID approach. The importance of retaining such properties as proper time and frequency marginals; time and frequency support along with proper group delay and instantaneous frequency will be discussed. The value of covariance with time and frequency shifts and scale changes will also be emphasized.