Time-frequency Representation Of Signal Research Articles

Blind single-channel lamb wave mode separation using independent component analysis on time-frequency signal representation

Guided waves are widely employed in non-destructive testing, but the presence of dispersion and multiple modes poses a challenge in detecting and separating the received signals, thereby affecting the performance of testing algorithms. Traditional methods for ultrasonic wave mode separation rely on time-frequency transforms, which often require extensive post-processing or the selection of specific frequency points for mode separation. In contrast, this paper introduces a blind separation method that utilizes independent component analysis to facilitate blind single-channel Lamb wave multimode separation. The proposed method demonstrates robust performance even under high noise power levels, while effectively localizing the source energy in the time-frequency domain. Numerical and experimental tests validate the effectiveness of the proposed method, showcasing its ability to successfully separate signals from instantaneous linear mixtures.

LaSNet: An end-to-end network based on steering vector filter for sound source localization and separation

In this paper, we propose a novel time-domain end-to-end network (LaSNet) for solving the problem of multiple sound sources localization (SSL) and separation based on microphone array. The traditional time-frequency (T-F) signal representation is subject to various prior conditions and fails to separate the different sound signal components. Even the data-driven neural network does not develop an effectively integrated approach where localization and separation interplay to serve both challenge. To address the aforementioned issue, we propose a novel approach that involves the implementation of a Separation Driving Localization Network (SDLNet). This framework operates by extracting latent features from a separation network and subsequently employing them in the context of a localization network. Then we propose a simple multi-task network for both SSL and separation. Through the analysis of steering vector filter, we find that the localization and separation problems can be linked by the operation of pseudo-inverse (pinv). To facilitate a synergistic relationship between SSL and sound separation, while also enabling end-to-end network training, we develop a Pinv Module (PM). Fianlly, the Localization and Separation Network (LaSNet) structure of this paper is proposed. Inspired by the overlay mechanism of network, LasNet is extended to a multi-task and multi-layer network, in which separation task is divided into multiple subtasks. A fuzzy separation loss function is introduced for training multi-layer network. Numerical experiments demonstrate that the proposed method has a clearly better advantageous improvement than several well known models. LaSNet has greatly performance improvement in both separation and localization, and achieves at least 32% relative reduction in model size, compared with the baseline models.

Energy-Efficient Audio Processing at the Edge for Biologging Applications

Biologging refers to the use of animal-borne recording devices to study wildlife behavior. In the case of audio recording, such devices generate large amounts of data over several months, and thus require some level of processing automation for the raw data collected. Academics have widely adopted offline deep-learning-classification algorithms to extract meaningful information from large datasets, mainly using time-frequency signal representations such as spectrograms. Because of the high deployment costs of animal-borne devices, the autonomy/weight ratio remains by far the fundamental concern. Basically, power consumption is addressed using onboard mass storage (no wireless transmission), yet the energy cost associated with data storage activity is far from negligible. In this paper, we evaluate various strategies to reduce the amount of stored data, making the fair assumption that audio will be categorized using a deep-learning classifier at some point of the process. This assumption opens up several scenarios, from straightforward raw audio storage paired with further offline classification on one side, to a fully embedded AI engine on the other side, with embedded audio compression or feature extraction in between. This paper investigates three approaches focusing on data-dimension reduction: (i) traditional inline audio compression, namely ADPCM and MP3, (ii) full deep-learning classification at the edge, and (iii) embedded pre-processing that only computes and stores spectrograms for later offline classification. We characterized each approach in terms of total (sensor + CPU + mass-storage) edge power consumption (i.e., recorder autonomy) and classification accuracy. Our results demonstrate that ADPCM encoding brings 17.6% energy savings compared to the baseline system (i.e., uncompressed raw audio samples). Using such compressed data, a state-of-the-art spectrogram-based classification model still achieves 91.25% accuracy on open speech datasets. Performing inline data-preparation can significantly reduce the amount of stored data allowing for a 19.8% energy saving compared to the baseline system, while still achieving 89% accuracy during classification. These results show that while massive data reduction can be achieved through the use of inline computation of spectrograms, it translates to little benefit on device autonomy when compared to ADPCM encoding, with the added downside of losing original audio information.

Deep Learning-Based Modulation Recognition for Low Signal-to-Noise Ratio Environments

Automatic modulation classification (AMC), which plays a significant role in wireless communication, can recognize the modulation type of the received signal without large amounts of transmitted data and parameter information. Supported by deep learning, which is a powerful tool for functional expression and feature extraction, the development of AMC can be greatly promoted. In this paper, we propose a deep learning-based modulation classification method with 2D time-frequency signal representation. In our proposed method, signals which have been received are first analyzed by time-frequency based on continuous wavelet transform (CWT). Then, CWT images of received signals are obtained and input to the deep learning model for classifying. We create a new CWT image dataset including 12 modulation types of signals under various signal-to-noise ratio (SNR) environment to verify the effectiveness of the proposed method. The experimental results demonstrate that our proposed method can reach to a high classification accuracy over the SNR of −11 dB.

EEG-Based Mental Tasks Recognition via a Deep Learning-Driven Anomaly Detector.

This paper introduces an unsupervised deep learning-driven scheme for mental tasks' recognition using EEG signals. To this end, the Multichannel Wiener filter was first applied to EEG signals as an artifact removal algorithm to achieve robust recognition. Then, a quadratic time-frequency distribution (QTFD) was applied to extract effective time-frequency signal representation of the EEG signals and catch the EEG signals' spectral variations over time to improve the recognition of mental tasks. The QTFD time-frequency features are employed as input for the proposed deep belief network (DBN)-driven Isolation Forest (iF) scheme to classify the EEG signals. Indeed, a single DBN-based iF detector is constructed based on each class's training data, with the class's samples as inliers and all other samples as anomalies (i.e., one-vs.-rest). The DBN is considered to learn pertinent information without assumptions on the data distribution, and the iF scheme is used for data discrimination. This approach is assessed using experimental data comprising five mental tasks from a publicly available database from the Graz University of Technology. Compared to the DBN-based Elliptical Envelope, Local Outlier Factor, and state-of-the-art EEG-based classification methods, the proposed DBN-based iF detector offers superior discrimination performance of mental tasks.

Improving the automatic target recognition algorithm’s accuracy through an examination of the different time-frequency representations and data augmentation

Abstract This research focuses on an improved automatic target recognition algorithm for solving the classification challenge of ground-moving targets from pulsed-Doppler radar. First, it was studied how decision-making intervals affect the proposed algorithm. Second, the altering of the data augmentation process was investigated. Third, a consideration of the three time-frequency signal representations and finally the use of different deep learning models for the classification issues were examined. It is proven that the proposed algorithm can efficiently recognize all targets enclosed in the publicly available RadEch dataset, with 4 s of radar echoes. When the decision-making time is only 1 s, a classification probability of 99.9% was obtained, which is an improvement related to the other research studies in this area. Furthermore, when the decision-making time is reduced 16 times the classification accuracy is reduced by only 1.3%. Moreover, the proposed algorithm was successful on another dataset enclosing ground-moving targets from comparable pulsed-Doppler radar.

Signal time–frequency representation and decomposition using partial fractions

Summary The Z-transform of a complex time signal (or the analytic signal of a real signal) is equal to the Z-transform of a prediction error divided by the Z-transform of the prediction error operator. This inverse is decomposed into a sum of partial fractions, which are used to obtain impulse response operators formed by non-causal filters that complex-conjugate symmetric coefficients. The time components are obtained by convolving the filters with the original signal, and the peak frequencies, corresponding to the poles of the prediction error operator, are used for mapping the time components into frequency components. For non-stationary signals, this decomposition is done in sliding time windows, and the signal component values, in the middle of each window, are attributed to the peak value of its frequency response that corresponds to the pole of this partial fraction component. The result is an exact, but non-unique, time–frequency representation of the input signal. A sparse signal decomposition can be obtained by summing along the frequency axis in patches with similar characteristics in the time–frequency domain. The peak amplitude frequency of each new time component is obtained by computing a scalar prediction error operator in sliding time windows, resulting in a sparse time–frequency representation. In both cases, the result is a time–frequency matrix where an estimate of the frequency content of the input signal can be obtained by summation over the time variable. The performance of the new method is demonstrated with excellent results on a synthetic time signal, the LIGO gravitational wave signal and seismic field data.

High‐resolution time‐frequency representation for instantaneous frequency identification by adaptive Duffing oscillator

Time-frequency analysis of structural vibration responses provides essential information for structural system identification, modal updating, and condition assessment. However, spurious peaks introduced by the strong noise will significantly increase the false positive rate as well as compromise the sparse time-frequency signal representation. This paper proposes a high-resolution time-frequency representation approach for nonstationary signals polluted with strong noise. With a high sensitivity to detect slight frequency shift and an immunity to noise effect, the intermittent chaotic of Duffing oscillator system is introduced to accurately identify the time-varying instantaneous frequencies. Furthermore, an adaptive Duffing oscillator array is adopted to improve the instantaneous frequency identification efficiency. The feasibility and effectiveness of the proposed method are verified with numerical and experimental studies. Numerical studies are conducted on a multicomponent synthetic nonstationary signal as well as on a two-story shear building with time-varying stiffness under seismic loads. In experimental validations, the acceleration response of a laboratory bridge model under moving vehicle load is also analyzed by using the proposed approach to obtain the instantaneous frequency variations induced by the bridge–vehicle interaction. These results are compared with those obtained from a method based on empirical wavelet transform and Hilbert transform (EWT-HT), to highlight the superiority of the proposed approach in obtaining high-resolution time-frequency analysis results for nonstationary signals with strong noise.

APPLICATION OF WAVELET – NEURAL METHOD TO DETECT BACKLASH ZONE IN ELECTROMECHANICAL SYSTEMS GENERATING NOISES

This paper presents a method of identifying the width of backlash zone in an electromechanical system generating noises. The system load is a series of rectangular pulses of constant amplitude, generated at equal intervals. The need for identification of the backlash zone is associated with a gradual increase of its width during the drive operation. The study uses wavelet analysis of signals and analysis of neural network weights obtained from the processing without supervised learning. The time-frequency signal representations of accelerations of the mechanical load components were investigated.

Novel method of informative frequency band selection for vibration signal using Nonnegative Matrix Factorization of spectrogram matrix

• Novel technique is proposed to diagnose vibration data from rolling bearing. • It allows to isolate component of local damage from among other impulsive components. • Algorithm is based on nonnegative matrix factorization of the spectrogram matrix. • Results are based on vibration data measured on a bearing of a copper ore crusher. The problem of local damage detection in rotating machines is currently the highly important subject of interest in the field of condition monitoring. In the literature one can find many different strategies. One of the most common approaches is the vibration signal analysis aiming at informative frequency band selection. In case of simply structured signals classic methods (e.g. spectral kurtosis) are sufficient and return clear information about the damage. However, in real-world cases the signal is usually much more complicated. Indeed, such signals consist of many different components, for instance: damage-related cyclic impulses, heavy-tailed background noise etc. Hence, there is a growing need for robust damage detection methods. In this paper a novel method of informative frequency band selection is proposed. It utilizes the approach of Non-negative Matrix Factorization applied to time-frequency signal representation. The described algorithm is evaluated using simulated signal containing several different components, that resembles real-life vibration signal from copper ore crusher, as well as real-life signal measured on the crusher. Using the obtained structure of informative frequency band it is possible to filter particular components out of the original signal.

Multi-Resolution Common Fate Transform

The multi-resolution common fate transform (MCFT) is an audio signal representation useful for representing mixtures of multiple audio signals that overlap in both time and frequency. The MCFT combines the invertibility of a state-of-the-art representation, the common fate transform (CFT), and the multi-resolution property of the cortical stage output of an auditory model. Since the MCFT is computed based on a fully invertible complex time-frequency representation, separation of audio sources with high time-frequency overlap may be performed directly in the MCFT domain, where there is less overlap between sources than in the time-frequency domain. The MCFT circumvents the resolution issue of the CFT by using a multi-resolution two-dimensional (2D) filter bank instead of fixed-size 2D windows. This enables higher quality separation without the need to hand-tune the window size to the specific case. In this work, we describe the MCFT, discuss the properties of the MCFT with the aid of illustrative examples, and provide definitions and objective measures for two desirable representation properties: separability of source signals and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">clusterability</i> of components of each signal. The utility of the MCFT for source separation is illustrated by performing ideal masking on a comprehensive dataset of audio mixtures of musical tones played in unison, including audio samples from a wide pitch range and a variety of instruments/playing techniques. Results show that the ideal masks made in the MCFT domain yield better separability than those made in commonly used time-frequency signal representations as well as the CFT. The use of the MCFT also results in more reliable clusterability than the CFT in most cases.

Pilot Decontamination over Time Frequency and Space Domains in Multi-Cell Massive MIMO System

In this article, we show that Pilot contamination problem can be seen as a source separation problem using time, frequency, and space domains. Our method capitalizes on a nonunitary joint diagonalization of spatial quadratic time-frequency (STFD) signal representation to identify the desired and interfering users. We first compute the noise subspace from the STFD matrices selected appropriately. Secondly, we use the noise subspace obtained to estimate the Elevation (El) and the Azimuth (Az) angles for which the MUSIC cost function is maximized. Numerical simulations are provided to illustrate the effectiveness and the behavior of the proposed approach.

Intrinsic Mode Chirp Multicomponent Decomposition with Kernel Sparse Learning for Overlapped Nonstationary Signals Involving Big Data

We focus on the decomposition problem for nonstationary multicomponent signals involving Big Data. We propose the kernel sparse learning (KSL), developed for the T-F reassignment algorithm by the path penalty function, to decompose the instantaneous frequencies (IFs) ridges of the overlapped multicomponent from a time-frequency representation (TFR). The main objective of KSL is to minimize the error of the prediction process while minimizing the amount of training samples used and thus to cut the costs interrelated with the training sample collection. The IFs first extraction is decided using the framework of the intrinsic mode polynomial chirp transform (IMPCT), which obtains a brief local orthogonal TFR of signals. Then, the IFs curves of the multicomponent signal can be easily reconstructed by the T-F reassignment. After the IFs are extracted, component decomposition is performed through KSL. Finally, the performance of the method is compared when applied to several simulated micro-Doppler signals, which shows its effectiveness in various applications.

Fault diagnosis for analog circuits utilizing time-frequency features and improved VVRKFA

This paper proposes a novel scheme for analog circuit fault diagnosis utilizing features extracted from the time-frequency representations of signals and an improved vector-valued regularized kernel function approximation (VVRKFA). First, the cross-wavelet transform is employed to yield the energy-phase distribution of the fault signals over the time and frequency domain. Since the distribution is high-dimensional, a supervised dimensionality reduction technique—the bilateral 2D linear discriminant analysis—is applied to build a concise feature set from the distributions. Finally, VVRKFA is utilized to locate the fault. In order to improve the classification performance, the quantum-behaved particle swarm optimization technique is employed to gradually tune the learning parameter of the VVRKFA classifier. The experimental results for the analog circuit faults classification have demonstrated that the proposed diagnosis scheme has an advantage over other approaches.

An effective approach for structural damage localization in flexural members based on generalized S-transform

This paper presents a method for structural damage localization based on signal processing using generalized S-transform (SGS). The S-transform is the combinations of the properties of the short-time Fourier transform (STFT) and wavelet transform (WT) that has been developed over the last few years in an attempt to overcome inherent limitations of the wavelet and short time Fourier transform in Time-Frequency representation of non-stationary signals. The generalized type of this transform is the SGS-transform that has adjustable Gaussian window width in the time-frequency representation of signals. In this research, the SGS-transform has been employed due to its favorable performance in detection of the structural damages. The performance of the proposed method has been verified by means of three numerical examples and also the experimental data obtained from the vibration test of 8-DOFs mass–stiffness system. By way of the comparison between damage location obtained from the proposed method and simulation model, it was concluded that the method is sensitive to the damage existence and clearly demonstrates the damage location.

Time-Frequency Analysis for GNSSs: From interference mitigation to system monitoring

In this article, we discuss the important role of time-frequency (TF) signal representations in enhancing global navigation satellite system (GNSS) receiver performance. Both linear transforms and quadratic TF distributions (QTFDs) are considered. We review recent advances of antijam techniques that exploit the distinction in the TF signatures between the desired and undesired signals, enabling effective jammer excision with minimum distortion to the navigation signals. The characterization of jammers by their instantaneous frequencies (IFs) lends itself to sparse structures in the TF domain and, as such, invites compressive sensing (CS) and sparse reconstruction to aid in joint-variable domain jamming localization and suppression. Furthermore, the integration of the spatial domain with the TFDs, through the use of multiantenna receivers, permits the applications of space-time processing for effective jamming mitigation. The article also describes the fundamental role of TFDs in monitoring the performance of new GNSSs, including satellite clocks and ionospheric scintillation data. Real GNSS data collected in the presence of jamming are used to demonstrate the effectiveness of TF-based antijam approaches

Sparse Arrays and Sampling for Interference Mitigation and DOA Estimation in GNSS

This paper establishes the role of sparse arrays and sparse sampling in antijam global navigation satellite systems (GNSS). We show that both jammer direction of arrival estimation methods and mitigation techniques benefit from the design flexibility of sparse arrays and their extended virtual apertures or coarrays. Taking advantage of information redundancy, significant reduction in hardware and computational cost materializes when selecting a subset of array antennas without sacrificing jammer nulling or localization capabilities. In addition to the spatial array sparsity, antijam can utilize sparsity of jammers in the spatio–temporal frequency domains. By virtue of their finite number, jammers in the field of view are sparse in the azimuth and elevation directions. For the class of frequency modulated jammers, sparsity is also exhibited in the joint time-frequency signal representation. These spatial and signal characteristics have called for the development of sparsity-aware antijam techniques for the accurate estimation of jammer space-time-frequency signature, enabling its effective sensing and excision. Both theory and simulation examples demonstrate the utility of coarrays, sparse reconstructions, and antenna selection techniques for antijam GNSS.

Double Fourier analysis for Emotion Identification in Voiced Speech

We propose a novel analysis alternative, based on two Fourier Transforms for emotion recognition from speech. Fourier analysis allows for display and synthesizes different signals, in terms of power spectral density distributions. A spectrogram of the voice signal is obtained performing a short time Fourier Transform with Gaussian windows, this spectrogram portraits frequency related features, such as vocal tract resonances and quasi-periodic excitations during voiced sounds. Emotions induce such characteristics in speech, which become apparent in spectrogram time-frequency distributions. Later, the signal time-frequency representation from spectrogram is considered an image, and processed through a 2-dimensional Fourier Transform in order to perform the spatial Fourier analysis from it. Finally features related with emotions in voiced speech are extracted and presented.

A velocity synchrosqueezing transform for fault diagnosis of planetary gearboxes under nonstationary conditions

Time–frequency analysis is widely used in the field of machinery condition monitoring and fault diagnosis under nonstationary conditions. Among the time–frequency methods synchrosqueezing transform outperforms others in providing fine-resolution time–frequency representation. However, it suffers from time–frequency smear when analysing nonstationary signals. To address this issue, this paper proposes a new synchrosqueezing-transform-based method which works by (1) mapping the raw nonstationary vibration signal into a corresponding stationary angle domain signal to meet the stationarity requirement of the synchrosqueezing transform, (2) performing the synchrosqueezing transform of the corresponding signal and (3) restoring the time–frequency representation of the raw signal from the synchrosqueezing transform result of the corresponding signal. As the synchrosqueezing transform is applied to the stationary corresponding signal, the time–frequency smear is eliminated in the synchrosqueezing transform result of the corresponding signal and the final signal time–frequency representation. As such the proposed method can generate a smear-free time–frequency representation with fine time–frequency resolution and thus provide more reliable diagnosis decisions. A fast implementation algorithm is also developed to simplify the implementation of the proposed method. The effectiveness of the proposed method is validated using both simulated and experimental vibration signals of planetary gearboxes.

Field programmable gate arrays implementation of Dual Tree Complex Wavelet Transform.

Due to the inherent time-varying characteristics of physiological systems, most biomedical signals (BSs) are expected to have non-stationary character. Therefore, any appropriate analysis method for dealing with BSs should exhibit adjustable time-frequency (TF) resolution. The wavelet transform (WT) provides a TF representation of signals, which has good frequency resolution at low frequencies and good time resolution at high frequencies, resulting in an optimized TF resolution. Discrete wavelet transform (DWT), which is used in various medical signal processing applications such as denoising and feature extraction, is a fast and discretized algorithm for classical WT. However, the DWT has some very important drawbacks such as aliasing, lack of directionality, and shift-variance. To overcome these drawbacks, a new improved discrete transform named as Dual Tree Complex Wavelet Transform (DTCWT) can be used. Nowadays, with the improvements in embedded system technology, portable real-time medical devices are frequently used for rapid diagnosis in patients. In this study, in order to implement DTCWT algorithm in FPGAs, which can be used as real-time feature extraction or denoising operator for biomedical signals, a novel hardware architecture is proposed. In proposed architecture, DTCWT is implemented with only one adder and one multiplier. Additionally, considering the multi-channel outputs of biomedical data acquisition systems, this architecture is capable of running N channels in parallel.