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Time-frequency signal processing offers a significant advantage over temporal or frequency-only methods, but representations require optimisation for a given signal. Standard practice includes choosing the appropriate time-frequency distribution and fine-tuning its parameters, usually via visual inspection and various measures—the most commonly used ones are based on the Rényi entropies or energy concentration by Stanković. However, a discrepancy between the observed representation quality and reported numerical value may arise when the filter kernel has greater adaptability. Herein, a performance measure derived from the Abbot–Firestone curve similar to the volume parameters in surface metrology is proposed as the objective function to be minimised by the proposed minimalistic differential evolution variant that is parameter-free and uses a population of five members. Tests were conducted on two synthetic signals of different frequency modulations and one real-life signal. The multiform tiltable exponential kernel was optimised according to the Rényi entropy, Stanković's energy concentration and the proposed measure. The resulting distributions were mutually evaluated using the same measures and visual inspection. The optimiser demonstrated a reliable convergence for all considered measures and signals, while the proposed measure showed consistent alignment of reported numerical values and visual assessments. [ABSTRACT FROM AUTHOR]

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Numerous damage detection methods have been discovered to provide an early warning at the earliest possible stage against structural damage or any type of abnormality in the wind turbine system. In this paper, a comprehensive literature review is carried out in the field of damage detection for wind turbine systems. Several modern signal processing techniques including time-domain and frequency-domain analysis, joint time–frequency methods, entropy-based damage detection, supervisory control and data acquisition (SCADA), and machine learning approaches are all emphasized, and how to estimate the damage in wind turbine system by utilizing these various approaches is discussed. It is concluded that each of these methods offers its own unique merits and shortcomings in detecting certain types of damage with various levels of complexity. This research paper is aimed to inform the readers and experts about the damage detection techniques of the wind turbine system and fault diagnosis with various advanced signal processing methods. [ABSTRACT FROM AUTHOR]

The ideal time-frequency (TF) representation which distributes the total energy along the instantaneous frequency (IF) of a signal is essentially sparse. Motivated by the weighted sparse representation of the signal, we propose the ridge-aware weighted sparse TF representation (RWSTF) which involves some properties an ideal TF representation should satisfy, such as, highly concentrated TF representation, the signal reconstruction and acceptable computational cost. Based on a basic sparse TF model, we firstly use a weighted strategy to effectively highlight the TF ridges even for the weak components, then fast iterative shrinkage thresholding algorithm (FISTA) is applied to obtain an efficient numerical approximation for solving the model. Furthermore, we introduce a k-sparsity strategy for the adaptive selection of the regularization parameter. A simulation study shows that the proposed method not only has higher energy concentration, but also performs better on signal denoising than other standard TF approaches, especially for the signals with fast varying IF. Two real life examples confirm the potential of the proposed method. [ABSTRACT FROM AUTHOR]

Cross-term suppression in the Wigner distribution is a challenging task. Kernel based schemes are most widely used for reducing cross-terms. However, these schemes suffer from the intrinsic give and take between auto-term resolution and cross-term suppression. This paper presents a cross- term suppression scheme by combining directional filtering with image processing. This scheme retains the resolution of auto-term while significantly reducing cross-terms. The performance comparison with other methods demonstrates that the proposed method is superior compared to other methods in terms of cross-term suppression and energy concentration. [ABSTRACT FROM AUTHOR]

Background: Heart rate variability (HRV) is a widespread non-invasive technique to assess cardiac autonomic function. Time and frequency domain analyses have been used in HRV studies, and their interpretations are linked with both clinical prognostic and diagnostic information. Statistical and geometrical parameters, Fast Fourier Transform and Autoregressive based periodograms are commonly used approaches for the assessment of stationary RR intervals (RRi) signals. However, some conditions result in non-stationary HRV behavior such as the "tilt test" and exercise. This study presents the SinusCor, a new free software for HRV analysis that includes the classical time and frequency domain indices and also techniques for non-stationary data analyses in both time (i.e. root mean squared of successive differences; RMSSD calculated with moving segments) and frequency domains (i.e. time-frequency analysis).Results: An example of RRi was acquired from a young male subject and its time and frequency domain indices were calculated. Time-varying and time-frequency analyses were also presented using the RMSSD and total power, respectively. Validation of the present software against a standard software for HRV analysis (Kubios v 3.0.1) was also performed [SinusCor vs. Kubios: RMSSD-93.96 (41.55) vs. 93.96 (41.55) ms; SDNN-101.29 (29.03) vs. 101.29 (29.03) ms; LF-50.42 (19.76) vs. 50.56 (19.56) n.u.; HF-49.57 (19.76) vs. 49.38 (19.56) n.u.; LF/HF-1.38 (1.08) vs. 1.38 (1.07)].Conclusions: SinusCor might be a useful tool for classical stationary and non-stationary HRV analysis. [ABSTRACT FROM AUTHOR]

The time–frequency analysis of the tennis racket and hand vibrations is of great interest for discomfort and pathology prevention. This study aimed to (i) to assess the stationarity of the vibratory signal of the racket and hand and (ii) to identify the best mother wavelet to perform future time–frequency analysis, (iii) to determine if the stroke spin, racket characteristics and impact zone can influence the selection of the best mother wavelet. A total of 2364 topspin and flat forehand drives were performed by fourteen male competitive tennis players with six different rackets. One tri-axial and one mono-axial accelerometer were taped on the racket throat and dominant hand respectively. The signal stationarity was tested through the wavelet spectrum test. Eighty-nine mother wavelet were tested to select the best mother wavelet based on continuous and discrete transforms. On average only 25 ± 17%, 2 ± 5%, 5 ± 7% and 27 ± 27% of the signal tested respected the hypothesis of stationarity for the three axes of the racket and the hand respectively. Regarding the two methods for the detection of the best mother wavelet, the Daubechy 45 wavelet presented the highest average ranking. No effect of the stroke spin, racket characteristics and impact zone was observed for the selection of the best mother wavelet. It was concluded that alternative approach to Fast Fourier Transform should be used to interpret tennis vibration signals. In the case where wavelet transform is chosen, the Daubechy 45 mother wavelet appeared to be the most suitable. [ABSTRACT FROM AUTHOR]

This paper addresses the identification of the Dual Tone Multiple Frequency (DTMF) signal from real environments where the signal was corrupted during acquisition and transmission processes by using the sequential Bayesian filtering along with the time-frequency representation of time-series. The mathematical and statistical models were employed to estimate the frequency content embedded in the real DTMF signal. A sequential state-space framework, by treating each frequency component as a target to be tracked, that is developed in this work for the extraction of time-frequency information from time slice spectrograms provides excellent results, stemming from an efficient representation of the DTMF signals in the frequency domain. The paper also illustrates the accuracy of the estimates by displaying the probability density functions (PDFs) of the frequencies obtained from the filter. The performance of the proposed approach was compared to those of the conventional method. The comparison demonstrates a significant benefit of our method for DTMF signal identification under various noisy environments. [ABSTRACT FROM AUTHOR]

We propose a new method for underdetermined blind source separation based on the time-frequency domain. First, we extract the time-frequency points that are occupied by a single source, and then, we use clustering methods to estimate the mixture matrix A. Second, we use the parallel factor (PARAFAC), which is based on nonnegative tensor factorization, to synthesize the estimated source. Simulations using mixtures of audio and speech signals show that this approach yields good performance. [ABSTRACT FROM AUTHOR]

This paper focuses on the high resolution time-frequency distribution (TFD) of multicomponent signals with amplitude and frequency modulations, and a concise method named short-time sparse representation (STSR) is proposed. In STSR, both analysis and synthesis of the discrete signal can be achieved by exploiting the signal's sparsity in frequency domain at each time instant. In order to fasten the STSR procedure, an efficient sparse recovery algorithm named SL0 is applied, and the signal model for each sliding window is modified to form the same dictionary, which guarantees that the whole recovery procedure adapts to the matrix form. The performance of STSR is compared with other TFD techniques and assessed in various configurations. It is shown that both preferable representation and acceptable computational cost can be obtained. [ABSTRACT FROM AUTHOR]

In the low frequency range, the reverberation of a room should be characterized by the decay time, which can be determined experimentally by various methods. In order to make accurate and precise measurements, the differences between these methods and their advantages should be known and quantified. In this work, the performance of four linear and four adaptive time–frequency impulse response analysis methods was evaluated with the aim to find the most accurate method for characterizing the decays of the room modes. The methods were compared using generated Prony test signals with known modal properties and measured room impulse responses were also examined. The decay time using the selected time–frequency impulse response method was then estimated in three rooms and the measurement results were compared with interrupted sine tone methods. It has been shown that the choice of measurement setup and analysis parameters has an important influence on the estimation of the decay time and its modal frequency. The time–frequency impulse response method using the window width optimized Stockwell transform, the continuous wavelet transform, or the Morlet wave method were found to be the most robust methods, and their applicability is also enhanced by the fact that only a single measurement is required for the selected microphone position. The presented test methods could be used to evaluate the performance of other approaches for the evaluation of reverberation below the Schroeder frequency or the ability of measurement and signal processing techniques to characterize low frequency transient signals. • Research on time–frequency transforms for characterization of room impulse response. • Performance is tested on generated and real room impulse responses. • A time–frequency impulse response method for decay time measurement is proposed. • The method is compared to interrupted sine tone methods. • The time–frequency impulse response method is found to be the most robust. [ABSTRACT FROM AUTHOR]

Abstract: Commonly used time-frequency representations, like the short-time Fourier transform, the Wigner distribution and the higher order polynomial distributions, estimate the instantaneous frequency at the middle of the time-interval used in the analysis. For real time applications, like for example in radar signal processing, where the target parameters are estimated in the same way as the instantaneous frequency, the delay of a half of the considered interval may be unacceptable. Here, we propose a distribution that inherently estimates the instantaneous frequency at the end of the considered time interval. With a presented procedure for on-line implementation it can outperform other time-frequency representations for real time instantaneous frequency estimation. [Copyright &y& Elsevier]

Identification of vibration parameters from the analysis of the dynamic response of a stmcWa-e plays a key role in current health monitoring systems. This study evaluates the capabilities of the recently developed Synchrosqueezed Wavelet Transform (SWT) to extract instant frequencies and damping values from the simulated noise-contaminated response of a structure. Two approaches to estimate the modal damping ratio from the results of the SWT are presented. The results obtained are compared to other signal processing methods based on Continuous Wavelet (CWT) and Hilbert-Huang (HHT) transforms. It was found that the time-frequency representation obtained via SWT is sharped than the obtained using just the CWT and it allows a more robust extraction of the individual modal responses than using the HHT. However, the identification of damping ratios is more stable when the CWT coefficients are employed. [ABSTRACT FROM AUTHOR]

Abstract: Human gait is one of the biological features for human recognition. The key feature of gait can be acquired by analyzing the human echo signal to CW radar. Based on the data from the test CW gait radar, the methods for analyzing multi-component non-stationary signal are discussed in detail. The comparison among the application STFT, WVD, Pseudo-smoothed WVD and its improvements in gait signal are given, and the basic method for gait feature extraction based on time-frequency analysis is proposed. The results in this paper will be a well support for further research. [Copyright &y& Elsevier]

Sounds in the natural environment form an important class of biologically relevant non-stationary signals. We propose a dynamic spectral measure to characterize the spectral dynamics of such non-stationary sound signals and classify them based on rate of change of spectral dynamics. We categorize sounds with slowly varying spectral dynamics as simple and those with rapidly changing spectral dynamics as complex. We propose rate of spectral dynamics as a possible scheme to categorize sounds in the environment. [ABSTRACT FROM AUTHOR]

Abstract: Brain oscillations constitute a prominent feature of electroencephalography (EEG), in both physiological and pathological states. An efficient separation of oscillation from transient signals in EEG is important not only for detection of oscillations, but also for advanced signal processing such as source localization. A major difficulty lies in the fact that filtering transient phenomena can lead to spurious oscillatory activity. Therefore, in the presence of a mixture of transient and oscillatory events, it is not clear to which extent filtering methods are able to separate them efficiently. The objective of this study was to evaluate methods for separating oscillations from transients. We compared three methods: finite impulse response (FIR) filtering, wavelet analysis with stationary wavelet transform (SWT), time–frequency sparse decomposition with Matching Pursuit (MP). We evaluated the quality of reconstruction and the results of automatic detection of oscillations intermingled with transients. The emphasis of our study was on epileptic signals and single channel processing. In both simulations and on real data, FIR performed generally worse than the time–frequency methods. Both SWT and MP showed good results in separation and detection, each method having its advantages and its limitations. The SWT had good results in separation and detection of transients due to the time invariance property, but still did not completely resolve the frequency overlap for the oscillation during the time–frequency thresholding. The MP provides a sparse representation, and gave good results for simulated data. However, in the real data, we observed distortions introduced by the subtractive approach, and departure from dictionary waveforms. Future directions are proposed for overcoming these limitations. [Copyright &y& Elsevier]

Abstract: Fractional Fourier transform (FRFT) is a generalization of the Fourier transform, rediscovered many times over the past 100 years. In this paper, we provide an overview of recent contributions pertaining to the FRFT. Specifically, the paper is geared toward signal processing practitioners by emphasizing the practical digital realizations and applications of the FRFT. It discusses three major topics. First, the manuscripts relates the FRFT to other mathematical transforms. Second, it discusses various approaches for practical realizations of the FRFT. Third, we overview the practical applications of the FRFT. From these discussions, we can clearly state that the FRFT is closely related to other mathematical transforms, such as time–frequency and linear canonical transforms. Nevertheless, we still feel that major contributions are expected in the field of the digital realizations and its applications, especially, since many digital realizations of the FRFT still lack properties of the continuous FRFT. Overall, the FRFT is a valuable signal processing tool. Its practical applications are expected to grow significantly in years to come, given that the FRFT offers many advantages over the traditional Fourier analysis. [Copyright &y& Elsevier]

In the case of multicomponent signals with amplitude and frequency modulations, the idealized representation which consists of weighted trajectories on the time-frequency (TF) plane, is intrinsically sparse. Recent advances in optimal recovery from sparsity constraints thus suggest to revisit the issue of TF localization by exploiting sparsity, as adapted to the specific context of (quadratic) TF distributions. Based on classical results in TF analysis, it is argued that the relevant information is mostly concentrated in a restricted subset of Fourier coefficients of the Wigner-Ville distribution neighboring the origin of the ambiguity plane. Using this incomplete information as the primary constraint, the desired distribution follows as the minimum ℓ1-norm solution in the transformed TF domain. Possibilities and limitations of the approach are demonstrated via controlled numerical experiments, its performance is assessed in various configurations and the results are compared with standard techniques. It is shown that improved representations can be obtained, though at a computational cost which is significantly increased. [ABSTRACT FROM AUTHOR]

Abstract: We present an algorithm based on a short-term representation of the fractional Fourier transform which is highly suited to signals that contain multiple non-stationary components. To compare the time–frequency resolution of such signals using our proposed technique, we analyze several signals which contain multiple non-stationary components, including a synthetic signal and a bat echolocation signal. We demonstrate that our technique offers time–frequency representations with superior time–frequency resolution than several other established methods. [Copyright &y& Elsevier]

Ataxia is a genetic neurological disorder characterised by a neurodegenerative process affecting a motor cortex responsible for balance and coordination. Recently several genes that cause autosomal dominant ataxia development were identified. These abnormal genes share a common ability to produce abnormal ataxin proteins that can affect nerve cells in the cerebellum and spinal cord. Here, using the Resonant Recognition Model (RRM) based on signal processing, we analysed ataxin proteins and identified the characteristic features corresponding to their biological activities. The RRM is a physico-mathematical model developed for analysis of protein interactions. By incorporating Smoothed Pseudo Wigner–Ville distribution (SPWV) in the RRM, we can define the active regions along the protein molecule. The results showed that our computational predictions correspond closely with the experimentally identified locations of the active/binding sites for ataxin-1 and ataxin-3 protein groups. The results obtained provide a valuable insight into the functional performance of ataxin proteins. [ABSTRACT FROM AUTHOR]

• A new time–frequency methodology for the automatic detection of COVID-19 cough. • It can be applied in other respiratory diseases and for detecting Covid outbreaks. • The method obtained an accuracy close to 90%. • High performance was obtained in various sampling sources (UdL, UC, Virufy and Coswara). • The experiments validated the method as a generic proposal. Easy detection of COVID-19 is a challenge. Quick biological tests do not give enough accuracy. Success in the fight against new outbreaks depends not only on the efficiency of the tests used, but also on the cost, time elapsed and the number of tests that can be done massively. Our proposal provides a solution to this challenge. The main objective is to design a freely available, quick and efficient methodology for the automatic detection of COVID-19 in raw audio files. Our proposal is based on automated extraction of time–frequency cough features and selection of the more significant ones to be used to diagnose COVID-19 using a supervised machine-learning algorithm. Random Forest has performed better than the other models analysed in this study. An accuracy close to 90% was obtained. This study demonstrates the feasibility of the automatic diagnose of COVID-19 from coughs, and its applicability to detecting new outbreaks. [ABSTRACT FROM AUTHOR]

The characterization of non-stationary signal requires joint time and frequency information. However, time and frequency are a pair of non-commuting variables that cannot constitute a joint probability density in the time-frequency plane. The time-frequency distributions have difficult interpretation problems arising from negative and complex values or spurious components. In this paper, we get time-frequency information from the marginal distributions in rotated directions in the time-frequency plane. The rigorous probability interpretation of the marginal distributions is without any ambiguities. This time-frequency transformation is similar to the computerized axial tomography (CT or CAT) and is applied to signal analysis and signal detection and reveals a lot of advantages especially in the signal detection of the low signal/noise (S/N). [ABSTRACT FROM AUTHOR]

When physical models are of a high complexity, a signal processing approach is helpful for providing accurate information about a system and its failures. The session at this Conference entitled ‘Advanced Signal Processing and Condition Monitoring’ contains papers who propose new advanced signal processing methods in the context of condition monitoring, diagnostic and fault detection. The methods proposed tackle the analysis, modelling and/or detection of non-stationary and/or non-linear signals in time, frequency, time-frequency and/or time-scale domains using parametric, non-parametric and/or statistical approaches. Tools such as optimisation techniques can cope with the high non-linearity of the system to solve. The methods proposed are successful in decision-making and bring on a step up in real-life signal processing applications. Signals or considered models come from domains such as acoustics, vibroacoustics, mechanics and electrical engineering. This keynote paper outlines a structured session of the Fourth International Conference on Condition Monitoring, gives some insight in spectral and time-frequency analysis and, in particular, presents a way of modelling highly non-stationary signals having both non-linear amplitude and non-linear frequency modulations. [ABSTRACT FROM AUTHOR]

Inspired by the work on image processing by Perona and Malik, diffusion-based models were first investigated by Gonçalvès and Payot to improve the readability of Cohen class time-frequency representations. They rely on signal-dependent partial differential equations that yield adaptive smoothed representations with sharpened time-frequency components. Here, we demonstrate the versatility and utility of this family of methods, and we propose new adaptive diffusion processes to locally control both the orientation and the strength of smoothing. Our approach is an improvement on previous works as it provides a unified framework not only for the Cohen class but for the affine class as well. The latter is of particular interest because, except for some special techniques such as the reassignment method, no signal-dependent smoothing technique exists to process bilinear time-scale distributions, nor even a transposition of the adaptive optimal-kernel method proposed by Baraniuk and Jones. [ABSTRACT FROM AUTHOR]

This paper presents a family of hybrid time–frequency methods to be used as a tool for transient signal analysis. These methods are based on autoregressive models of the signal, and on the maximum likelihood method. A classical Wigner–Ville distribution and a parametric time–frequency methods are used for comparison purposes. The characteristics, advantages and disadvantages, of non-parametric, parametric and hybrid methods are discussed and their performances are compared by analysing actual data. The superiority of time–frequency resolution of the hybrid methods is pointed out over that of the parametric and non-parametric ones. Three practical examples of transient signals illustrate the discussion: the vibration signal issued from a damaged gearbox, a signal from a pendular scratch test presenting beating phenomenon and the vibration signal measured in an electrical motor during start-up. [Copyright &y& Elsevier]

We propose and discuss a complete framework for estimating significant changes in the average time-frequency density of energy of event-related signals. Addressed issues include estimation of time-frequency energy density (matching pursuit and spectrogram), choice of resampling statistics to test the hypothesis of change in one small region (reset), and correction for multiplicity (false discovery rate). We present estimation of the significance of event-related electroencephalograph desynchronization and synchronization (ERD/ERS) in the time-frequency plane. [ABSTRACT FROM AUTHOR]

We address the issue of the relation between local quantities and the uncertainty principle. We approach the problem by defining local quantities as conditional standard deviations, and we relate these to the uncertainty product appearing in the standard uncertainty principle. We show that the uncertainty product for the avenge local standard deviations is always less than or equal to the standard uncertainty product and that it can be arbitrarily small. We apply these results to the short-time Fourier transform/spectrogram to explore the commonly held notion that the uncertainty principle somehow limits local quantities. We show that, indeed, for the spectrogram, there is a lower bound on the local uncertainty product of the spectrogram due to the windowing operation of this method. This limitation is an inherent property of the spectrogram and is not a property of the signal or a fundamental limit. We also examine the local uncertainty product for a large class of time-frequency distributions that satisfy the usual uncertainty principle, including the Wigner distribution, the Choi-Williams distribution, and many other commonly used distributions. We obtain an expression for the local uncertainty product in terms of the signal and show that for these distributions, the local uncertainty product is Less than that of the spectrogram and can be arbitrarily small. Extension of our approach to an entropy formulation of the uncertainty principle is also considered. [ABSTRACT FROM AUTHOR]

This article deals with a method based on the fractional Fourier transform (FRFT) to estimate the parameters of linear chirps. Appropriate filtering in fractional domains based on this method allows to extract linear chirps out of a multicomponent and noisy signal. This method is used to analyse the propagation of acoustic wave in a dispersive medium (lattice made up of Helmholtz resonators). The nonlinear effects due to the Helmholtz resonators are highlighted. The frequency dependance of the nonlinear processes is shown thanks to the extraction method proposed. [Copyright &y& Elsevier]

The paper presents an analysis and overview of vertex–frequency analysis, an emerging area in graph signal processing. A strong formal link of this area to classical time–frequency analysis is provided. Vertex–frequency localization-based approaches to analyzing signals on the graph emerged as a response to challenges of analysis of big data on irregular domains. Graph signals are either localized in the vertex domain before the spectral analysis is performed or are localized in the spectral domain prior to the inverse graph Fourier transform is applied. The latter approach is the spectral form of the vertex–frequency analysis, and it will be considered in this paper since the spectral domain for signal localization is well ordered and thus simpler for application to the graph signals. The localized graph Fourier transform is defined based on its counterpart, the short-time Fourier transform, in classical signal analysis. We consider various spectral window forms based on which these transforms can tackle the localized signal behavior. Conditions for the signal reconstruction, known as the overlap-and-add (OLA) and weighted overlap-and-add (WOLA) methods, are also considered. Since the graphs can be very large, the realizations of vertex–frequency representations using polynomial form localization have a particular significance. These forms use only very localized vertex domains, and do not require either the graph Fourier transform or the inverse graph Fourier transform, are computationally efficient. These kinds of implementations are then applied to classical time–frequency analysis since their simplicity can be very attractive for the implementation in the case of large time-domain signals. Spectral varying forms of the localization functions are presented as well. These spectral varying forms are related to the wavelet transform. For completeness, the inversion and signal reconstruction are discussed as well. The presented theory is illustrated and demonstrated on numerical examples. [ABSTRACT FROM AUTHOR]