Time-varying Spectral Content Research Articles

Impaired Cortical Tracking of Speech in Children with Developmental Language Disorder.

In developmental language disorder (DLD), learning to comprehend and express oneself with spoken language is impaired, but the reason for this remains unknown. Using millisecond-scale magnetoencephalography recordings combined with machine learning models, we investigated whether the possible neural basis of this disruption lies in poor cortical tracking of speech. The stimuli were common spoken Finnish words (e.g., dog, car, hammer) and sounds with corresponding meanings (e.g., dog bark, car engine, hammering). In both children with DLD (10 boys and 7 girls) and typically developing (TD) control children (14 boys and 3 girls), aged 10-15 years, the cortical activation to spoken words was best modeled as time-locked to the unfolding speech input at ∼100 ms latency between sound and cortical activation. Amplitude envelope (amplitude changes) and spectrogram (detailed time-varying spectral content) of the spoken words, but not other sounds, were very successfully decoded based on time-locked brain responses in bilateral temporal areas; based on the cortical responses, the models could tell at ∼75-85% accuracy which of the two sounds had been presented to the participant. However, the cortical representation of the amplitude envelope information was poorer in children with DLD compared with TD children at longer latencies (at ∼200-300 ms lag). We interpret this effect as reflecting poorer retention of acoustic-phonetic information in short-term memory. This impaired tracking could potentially affect the processing and learning of words as well as continuous speech. The present results offer an explanation for the problems in language comprehension and acquisition in DLD.

A Scalable Systolic Accelerator for Estimation of the Spectral Correlation Density Function and Its FPGA Implementation

The spectral correlation density (SCD) function is the time-averaged correlation of two spectral components used for analyzing periodic signals with time-varying spectral content. Although the analysis is extremely powerful, it has not been widely adopted in real-time applications due to its high computational complexity. In this article, we present an efficient FPGA implementation of the FFT accumulation method (FAM) for estimating the SCD function and its alpha profile. The implementation uses a linear systolic array with a bi-directional datapath consisting of DSP-based processing elements (PEs) with a dedicated instruction schedule, achieving a PE utilization of 88.2%. The 128-PE implementation achieves a clock frequency in excess of 530 MHz and consumes 151K LUTs, 151K FFs, 264 BRAMs, 4 URAMs, and 1,054 DSPs, which is less than 36% of the logic fabric on a Zynq UltraScale+ XCZU28DR-2FFVG1517E RFSoC device. It has a modest 12.5W power consumption and an energy efficiency of 4,832 MOPS/W, which is 20.6× better than the published state-of-the-art GPU implementation. In terms of throughput, it achieves 15,340 windows/s (15,340 windows/s × 2,048 samples/window = 31.4 MS/s), which is a 4.65× improvement compared to the above-mentioned GPU implementation and 807× compared to an existing hybrid FPGA-GPU implementation.

Enhancing gearbox vibration signals under time-varying operating conditions by combining a whitening procedure and a synchronous processing method

Condition monitoring is very important to avoid unexpected breakdowns of expensive rotating machines found in the power generation and mining industries. The fault information in vibration signals is often buried in low energy frequency bands. In addition to this, time-varying operating conditions and the presence of impulsive components result in the signal to have time-varying spectral content, which impedes the condition inference process. The instantaneous power spectrum is a powerful method that for bearing and gear damage detection under time-varying operating conditions. In this work, we propose a new method of using the instantaneous power spectrum for improved fault diagnosis under time-varying conditions by enhancing the fault information in the vibration signals. It is shown on experimental datasets that the proposed method enhances the fault information in the signal, whereafter it can be used to obtain reliable condition indicators under time-varying operating conditions.

Adaptive estimation and sparse sampling for graph signals in alpha-stable noise

In the graph signal processing literature, most methods were developed based on the assumption of Gaussian noise since it can lead to computationally efficient and mathematically tractable solutions. Unfortunately, the Gaussian distribution cannot capture the sharp spikes and tail heaviness of the signal noise in various natural phenomena. The α-stable distribution is a generalization of the Gaussian distribution and is a more appropriate model for such impulsive heavy-tailed noise. In this paper, we consider the problem of adaptive estimation and sparse sampling for signals defined over graphs in the presence of impulsive α-stable noise. To tackle the problems associated with α-stable noise, the graph signal estimation problem is formulated as a minimum dispersion (MD)-based optimization. A novel adaptive least mean pth power (LMP) algorithm is proposed for robust estimation of band-limited graph signals from partial observations in α-stable noise environments. The mean square performance of the proposed LMP algorithm is theoretically analyzed. To handle the case of band-limited graph signals with unknown and time-varying bandwidth and spectral contents, the sparse nature of the Graph Fourier transform of the signal is exploited to develop an adaptive graph sampling technique. Specifically, the proposed sparse sampling technique identifies the spectral signal support via sparse online estimation building on the iterative shrinkage-thresholding algorithm. Numerical simulation studies are presented to corroborate the performance advantages of the proposed adaptive estimation and sparse sampling algorithms.

Accurate diagnosis of term–preterm births by spectral analysis of electrohysterography signals

Preterm delivery contributes to an increased risk of fetal and maternal death as well as several health deficiencies, thereby requiring special care and treatment that result in high financial costs. It is therefore of key importance to diagnose preterm delivery in advance in order to avoid or minimize its undesirable consequences.This paper proposes a novel method for non-invasive diagnosis of preterm delivery based on the classification of electrohysterography (EHG) signals. First, the EHG signal, which is related to the electrical activity of uterine muscles is recorded from the maternal fundus using surface electrodes. Then, the signal is sliced into frames for spectral analysis. Next, spectral analyses of the individual EHG signal frames are carried out and centroid frequencies of the frames are computed, establishing the elements of a feature vector that represents the time-varying spectral content of the EHG signal. Finally, this feature vector is employed for the classification of the underlying EHG signal for term–preterm diagnosis.The efficiency of the proposed approach is evaluated and compared with representative methods from the literature. Our results demonstrate that the proposed approach exhibits superior performance over other methods.

Non-linear auto-regressive models for cross-frequency coupling in neural time series.

We address the issue of reliably detecting and quantifying cross-frequency coupling (CFC) in neural time series. Based on non-linear auto-regressive models, the proposed method provides a generative and parametric model of the time-varying spectral content of the signals. As this method models the entire spectrum simultaneously, it avoids the pitfalls related to incorrect filtering or the use of the Hilbert transform on wide-band signals. As the model is probabilistic, it also provides a score of the model “goodness of fit” via the likelihood, enabling easy and legitimate model selection and parameter comparison; this data-driven feature is unique to our model-based approach. Using three datasets obtained with invasive neurophysiological recordings in humans and rodents, we demonstrate that these models are able to replicate previous results obtained with other metrics, but also reveal new insights such as the influence of the amplitude of the slow oscillation. Using simulations, we demonstrate that our parametric method can reveal neural couplings with shorter signals than non-parametric methods. We also show how the likelihood can be used to find optimal filtering parameters, suggesting new properties on the spectrum of the driving signal, but also to estimate the optimal delay between the coupled signals, enabling a directionality estimation in the coupling.

Parametric Time-Frequency Map and its Processing for Local Damage Detection in Rotating Machinery

The detection of local damage in rotating machinery (gears, bearings) via vibration signal analysis is one of the most powerful techniques in condition monitoring. However, in some cases, especially in heavy industrial machinery, it is difficult to detect damage because of the poor signal-to-noise ratio of the measured vibration. Therefore it is necessary to use unconventional advanced techniques to enhance the signal. In this paper, a novel approach based on parametric time-frequency analysis and further processing for: i) time-varying spectral content modelling, ii) the identification of informative frequency bands by statistical analysis, iii) local damage detection and iv) cycle identification via cepstral analysis, is presented. The proposed procedure is validated using real vibration data from bearings and gearboxes. It is worth noting that this methodology can be also successfully used in time-varying speed conditions (with limited fluctuation).

A Variable Bandwidth Filter for Estimation of Instantaneous Frequency and Reconstruction of Signals With Time-Varying Spectral Content

The notion of “instantaneous frequency” is utilized in processing signals with time-varying spectral content. Specifically, a variable bandwidth filter (VBF) and some related spectral analysis tools are proposed to handle a multicomponent signal whose components interact with each other in the time-frequency (TF) domain. In the analysis, a multicomponent signal is decomposed into its components by estimating local instantaneous frequencies (IFs). In order to construct the proposed filter, we define a differential operator composed of the derivative operator and a positive time-varying coefficient. An extended Fourier transform (EFT) and its functional relations are derived to exploit the newly defined differential operator and the VBF in some weighted vector spaces. Further, a heterogeneous TF distribution is constructed by a short-time EFT to utilize as a criterion for identifying whether an estimated IF is intrinsic or not and repairing a suspect estimate of IF. To confirm usefulness of the EFT and the VBF, we conduct several numerical simulations for spectral localization of an AM-FM signal and for estimation of local IFs, and then, for decomposition of a multicomponent signal into its components with their resolving powers to be compared.

Space–time–frequency analysis of EEG data using within-subject statistical tests followed by sequential PCA

A new method is developed for analyzing the time-varying spectral content of EEG data collected in cognitive tasks. The goal is to extract and summarize the most salient features of numerical results, which span space, time, frequency, task conditions, and multiple subjects. Direct generalization of an established approach for analyzing event-related potentials, which uses sequential PCA followed by ANOVA to test for differences between conditions across subjects, gave unacceptable results. The new method, termed STAT-PCA, advocates statistical testing for differences between conditions within single subjects, followed by sequential PCA across subjects. In contrast to PCA-ANOVA, it is demonstrated that STAT-PCA gives results which: 1) isolate task-related spectral changes, 2) are insensitive to the precise definition of baseline power, 3) are stable under deletion of a random subject, and 4) are interpretable in terms of the group-averaged power. Furthermore, STAT-PCA permits the detection of activity that is not only different between conditions, but also common to both conditions, providing a complete yet parsimonious view of the data. It is concluded that STAT-PCA is well suited for analyzing the time-varying spectral content of EEG during cognitive tasks.

Description and Simulation of Nonstationary Processes Based on Hilbert Spectra

A new method is proposed for the description and simulation of nonstationary random processes based on Hilbert spectra of their sample observations. A sample of a random process is first decomposed into intrinsic mode functions (IMFs) by the method of empirical mode decomposition. The Hilbert transforms of the IMFs yield the instantaneous amplitude and frequency, from which the Hilbert spectrum can be obtained as a function of time and frequency. The average of the Hilbert spectra over the samples is then defined as the Hilbert spectrum of the process and used as the target in the simulation of the process. The method is also extended to vector random processes. Unlike current procedures such as those based on the evolutionary process, no assumptions of functional forms for the spectra are necessary which are unknown a priori; and no assumptions of piecewise stationarity and egodicity of the process are required in parameter estimation. Applications to spectral characterization and simulation of multivariate earthquake ground motions show that the Hilbert spectra give a clear description of the time-varying spectral content of the motions and the simulated samples represent an accurate statistical image of the records. The response spectra compare well with those of the records and retain the jagged look. The method has great potential for engineering applications when dealing with nonstationary, nonlinear random processes.

Quantification of the dynamic behavior over time of narrow-band components present in heart rate variability by means of the instantaneous amplitude and frequency

The statistical properties of the time- and frequency-domain characteristics of heart rate variability are known to vary over time. A method is presented to compute the time-varying spectral contents of the characteristic narrow-band frequency components of heart rate variability by means of the instantaneous amplitude and frequency at an optimal time resolution. The instantaneous frequency may show oscillatory, but also irregular periods in time. An index of the instantaneous bandwidth is computed to discriminate between oscillatory and irregular periods and to correct the instantaneous amplitude and frequency for irregular periods.

The instantaneous frequency of cardiovascular time series: a comparison of methods

The instantaneous frequency (IF) of cardiovascular time series is used to describe the time-varying spectral contents of the characteristic frequency bands that are of interest for psychophysiological and cardiovascular research. Four methods to compute IF of band-limited, monocomponent, and analytical cardiovascular time series were compared by means of simulated time series contaminated with additive noise. These four methods are: the method using the inverse Fourier transform of uncorrelated time-slices of the Wigner–Ville distribution, the discrete time-frequency transform, the circular mean direction of the time-slices of the Wigner–Ville distribution, and the central finite difference of the phase. The time resolution of the estimates is optimal and is inversely related to the bandwidth of the frequency components, as given by the uncertainty principle of Gabor. At periods in time where the signal fulfills the requirements of the model signal, the four estimates of IF are numerically equal; only the circular mean direction showed a slight deviation from the other estimates. Although the estimates of IF differ at sudden phase shifts at low amplitude, i.e. at points where the signal locally does not comply with the requirements of the model signal, overall the four methods produce comparable estimates of IF of a cardiovascular time series at an optimal time resolution.

Spectral estimation of nonstationary ARMA processes using the evolutionary cepstrum

The spectral estimation problem of nonstationary autoregressive moving-average (ARMA) processes is considered and a new method is proposed for the estimation of the time-varying spectral content of such signals. The proposed method can be viewed as an extension of the estimator proposed earlier by the authors to the time-varying case. The AR part of the model is estimated by solving the time-varying modified Yule-Walker equations using an estimated time-varying autocorrelation function. An evolutionary cepstrum estimator is proposed, which is then used in a simple recursion to obtain the MA parameters of the model.

Parametric TFR via windowed exponential frequency modulated atoms

We propose a new atom, namely, the dilated and translated windowed exponential frequency modulated functions (FM/sup m/let) for compactly characterizing both the signal's time-invariant and time-varying spectral contents. The superiority of the proposed method to some existing time-frequency distributions (TFDs) is demonstrated using a bat sonar signal.

Instantaneous spectral moments

Density functions find application in many fields of science, math and engineering. In many cases, the density can be sufficiently characterized by some of its moments, particularly the mean, variance, skew and kurtosis. In signal analysis, densities of interest are the instantaneous power of the signal, the spectral density, and for signals with time-varying spectral content, the joint time–frequency density. As with densities in general, these signal densities may also be characterized by their low-order moments. For the case of the joint density, the moments are conditional moments, e.g., the mean frequency at a particular time. The first- and second-conditional moments of a time–frequency density have been well-studied in the past two decades; the third, fourth and higher conditional moments have not. In this paper, we propose candidates, utilizing an operator-theoretic approach, for the instantaneous spectral moments of a signal, in terms of its amplitude and phase. From these instantaneous spectral moments, we obtain expressions for the instantaneous spectral mean, variance, skew and kurtosis. We also address the question of designing kernels in the Cohen class of time–frequency distributions to obtain distributions with these moments.

Advances in Time-Frequency Analysis of Biomedical Signals

The frequency content of many biomedical signals can change rapidly with time. Conventional Fourier spectral analysis techniques are insufficient for analyzing the time-varying spectral content of these signals. By mapping a one-dimensional function of time (or frequency), the time-frequency representation can localize the signal energy in both the time and frequency directions. It has been shown that many biomedical signal problems may benefit from time-frequency analysis. The objective of this paper is to review the advances in time-frequency analysis of biomedical signals. Relevant theoretical methodologies and practical considerations are introduced, and five application areas are reviewed: electroencephalography (EEG), electrocardiography, phonocardiography, electrogastrography, and electromyography.