Discrete Time-Frequency Signal Analysis and Processing Techniques for Non-Stationary Signals

Spinal somatosensory evoked potential (SSEP) has been employed to monitor the integrity of the spinal cord during surgery. To detect both temporal and spectral changes in SSEP waveforms, an investigation of the application of time-frequency analysis (TFA) techniques was conducted. SSEP signals from 30 scoliosis patients were analysed using different techniques; short time Fourier transform (STFT), Wigner-Ville distribution (WVD), Choi-Williams distribution (CWD), cone-shaped distribution (CSD) and adaptive spectrogram (ADS). The time-frequency distributions (TFD) computed using these methods were assessed and compared with each other. WVD, ADS, CSD and CWD showed better resolution than STFT. Comparing normalised peak widths, CSD showed the sharpest peak width (0.13+/-0.1) in the frequency dimension, and a mean peak width of 0.70+/-0.12 in the time dimension. Both WVD and CWD produced cross-term interference, distorting the TFA distribution, but this was not seen with CSD and ADS. CSD appeared to give a lower mean peak power bias (10.3%+/-6.2%) than ADS (41.8%+/-19.6%). Application of the CSD algorithm showed both good resolution and accurate spectrograms, and is therefore recommended as the most appropriate TFA technique for the analysis of SSEP signals.

An empirical signal separation algorithm for multicomponent signals based on linear time-frequency analysis

Non-stationary and nonlinear signals, which can bring important applications in chaotic dynamics, and are found in several scientific and engineering fields. Several processing techniques have been used to understand and extract information from these signals, and the literature shows that time-frequency analysis techniques are suitable tools for this characterization. They allow to examine the time-varying characteristics of the signals. In this chapter, we will explore time-frequency methods applied especially to nonlinear signals. First, we discuss the diverse range of dynamical systems. Then, we introduce the classical time-frequency methods, including the Short-Time Fourier Transform, the Wavelet Transform, the Hilbert Transform, and the Wigner-Ville distribution. These methods have been widely used in the literature in the study of non-stationary operations. Thus, we present emerging methods of time-frequency analysis, taking advantage of post-processing and synchrosqueezing techniques to improve the accuracy and resolution of the time-frequency representation. We present a comprehensive analysis of these emerging methods, comparing them with classical approaches to show their contributions. Our main goal is to highlight the capabilities of these emerging time-frequency analysis methods in capturing and understanding chaotic patterns in signals.

Time-frequency representation and spectral features extraction from a digitally recorded ground motion time history of an earthquake is cornerstone in earthquake engineering signal processing and interpretation. Recently developed time-frequency analysis (TFA) techniques are one of the most suitable techniques for the spectral estimation of signals whose frequency content varies with time. The most often used TFA techniques are short-term Fourier transform, Gabor transform, wavelet transform, Wigner-Ville distribution, Choi-William distribution, and cone shape distribution. The spectrograms of TFA reveal better spectral estimation in time-frequency domain and hence recommended to estimate local frequencies, dominate frequency and their incident time. Moreover, the time of occurrence of frequency component corresponding to maximum energy burst as well as its variation with time can also be identified. Results obtained from TFA techniques shows better picture of the spectral content in the data than the other conventional techniques.

It is very useful to study the signals radiated from corona discharges for the purposes of high-voltage line monitoring. Time-frequency analysis can clearly reveal the time-varying spectrum characteristics of such signals, which is very useful for analyzing and processing the non-linear and non-stationary weak signals, such as the signals radiated from corona discharges. Several time-frequency analysis methods, such as the Short-Time Fourier Transform (STFT), Wigner-Ville distribution and the Hilbert-Huang Transform (HHT) and so on, are used in this paper. The simulation data with the same and different amplitudes are comparatively analyzed by these time-frequency distribution methods. It can be concluded that the time-frequency analysis method based on HHT is more efficient to identify and suitable for the non-linear and non-stationary weak signals.

The Wigner-Ville distribution (WVD) is a widely used time-frequency analysis (TFA) technique in non-stationary signal processing. However, as signal bandwidths increase, the low throughput of traditional serial architectures hinders real-time WVD processing. In this paper, we propose a novel dual-channel, fully parallel WVD architecture based on data shifting method. We comprehensively tap into the parallel potential in the WVD algorithm and present the corresponding data flow graph. By utilizing a symmetric dual-channel structure, we significantly streamline the generation and combination of autocorrelation sequences, while halving the total number of complex multiplications and FFTs. Additionally, we develop a memory-based, three-stage autocorrelation generator using a data-shifting technique, thereby obviating the necessity for address generation stages. Implementation results show that our design achieves a 95% latency reduction compared to the state-of-the-art WVD architectures, attaining a maximum clock frequency of 322 MHz on a Xilinx UltraScale+ FPGA. The proposed architecture holds substantial potential for augmenting the real-time processing of wide-band signals.

Time-frequency (TF) characterization of electromyographic (EMG) bursts is essential for accurately assessing muscle function, particularly when the signals exhibit a high degree of nonstationarity. In this exploratory study, we investigated the temporal dynamics of the spectral components associated with short-latency EMG bursts using several TF analysis techniques. Specifically, we compared the performance and interpretability of spectrograms obtained via the short-time Fourier transform (STFT), the continuous wavelet transform (CWT), and noise-assisted multivariate empirical mode decomposition (NA-MEMD), applied to EMG signals recorded from the biceps femoris muscle of freely moving rats in an animal model of Parkinson's disease, acquired using chronically implanted bipolar electrodes during treadmill locomotion. For each method, we evaluated its effectiveness in capturing transient variations in frequency content, the stability of extracted features across bursts, and the extent to which these features reflect physiologically meaningful aspects of muscle activation. The results show that TF approaches reveal complementary information about burst structure; NA-MEMD provides greater adaptability to nonlinear and nonstationary components, whereas STFT- and CWT-based representations offer more controlled and comparable analyses. Overall, these findings highlight the value of TF analysis as a methodological tool for evaluating muscle function and provide a solid foundation for selecting analytical strategies in studies where EMG bursts exhibit complex and highly variable spectral profiles.

According to the non-stationary of PD pulse signal, the Joint Time-Frequency Analysis (JTFA) is put forward to process the signal to obtain their characteristics in time-frequency domain. At present, the Wigner-Ville Distribution (WVD) which belongs to the Cohen class Time-Frequency Energy Distribution is popular in processing the non-stationary signals. So the simulation PD pulse is chosen as the subject investigated to study on the original WVD, Smoothing-Pseudo WVD (SPWVD) and Rearranged-Smoothing-Pseudo WVD (RSPWVD) in this paper. The results show that WVD provides a high sensitivity to variation in short duration of non-stationary PD signal, which is available to extract the time-varying information. And the SPWVD can remove the interference cross-terms with reducing the time-frequency resolution, which is caused by bilinear function. For having good time-frequency concentration, the RSPWVD provides a powerful tool to evaluate parameters for single PD pulse shape.

Short-time Fourier transform and superoscillations

A method and system of real-time feedback and analyzing Electroencephalogram (EEG) using short-time Fourier transform (STFT) and coherence analysis is presented in this paper. The system composition of hardware and software are described. By the utilization of this method and system, the EEG's real-time time-frequency distribution (TFD) is obtained, and the EEG temporal spectral 3-dimension array is displayed on computer's screen for EEG realtime feedback. The time-frequency analysis (TFA) such as Wigner-Ville distribution (WVT) and wavelet transform (WT), has been successfully applied in some biomedical signals to detect both temporal and spectral features of biomedical signals. But real-time realization of TFA is difficult since the computation complication of WVT and WT. By using the STFT algorithm, we develop a system for the EEG feedback and TFA in real-time. This system may be used for EEG biofeedback, and possesses the value of clinical practice.

Fault signals of motors is non-stationary typically. Conventional Fourier transform method can't meet the demand of fault signals extraction. Time-frequency analysis (TFA) based motor fault diagnosis methods, which can identify rotor faults by detecting time-varying frequency components of stator current signals, have been very important signal processing techniques. This paper proposes a new motor fault detection method based on multiple window S-method TFA. Slepian sequences are applied as window functions. Compared with common short-time Fourier transform (STFT) and Wigner-Ville distribution (WVD), multiple window S-method TFA provides better time-frequency concentration and cross-term suppression performances, thus improving accuracy rate of motor rotor fault detection. Taking rotor dynamic eccentricity fault as an example, the validity of method is demonstrated.

In ultrasonic NDE applications, it is challenging to analyze ultrasonic backscattered signal in presence of high scattering noise. The ultrasound trace embodies the shape, size and orientation of reflectors and reveals the physical property of propagation path. The signal loss due to the effect of attenuation and scattering makes ultrasonic backscattered signal nonstationary. Therefore, a proper signal analysis technique is needed. As an effective tool of nonstationary signal analysis, time-frequency (TF) signal representations have been used in many applications, including ultrasound NDE. In this paper, other time-frequency analysis techniques have been reviewed. Especially, a model-based TF analysis and parameter estimation technique is discussed. Simulation and experimental results have shown its effectiveness in signal decomposition. Additionally two different models, i.e., chirplet model and Gabor model are compared in terms of energy compact in time-frequency representation of ultrasonic NDE signals.

The monitoring of the evolution of structural dynamic response under transient loads must be carried out to understand the physical behaviour of building subjected to earthquake ground motion, as well as to calibrate numerical models simulating their dynamic behaviour. Fourier analysis is one of the most used tools for estimating the dynamic characteristics of a system. However, the intrinsic assumption of stationarity of the signal imposes severe limitations upon its application to transient earthquake signals or when the dynamic characteristics of systems change over time (e.g., when the frequency of vibration of a structure decreases due to damage). Some of these limitations could be overcome by using the Short Time Fourier Transform (STFT). However, the width of the moving window adopted for the analysis has to be fixed as a function of the minimum frequency of interest, using the best compromise between resolution in both the time and frequency domains. Several other techniques for time-frequency analysis of seismic signals recorded in buildings have been recently proposed. These techniques are more suitable than the STFT for the application described above, although they also present drawbacks that should be taken into account while interpreting the results. In this study, we characterize the dynamic behaviour of the Falkenhof Tower (Potsdam, Germany) while forced by ambient noise and vibrations produced by an explosion. We compare the results obtained by standard frequency domain analysis with those derived by different time-frequency methods. In particular, the results obtained by the standard Transfer Function method, Horizontal to Vertical Spectral Ratio (HVSR), Short Time Fourier Transform (STFT), Empirical Mode Decomposition (EMD) and S-Transform are discussed while most of the techniques provide similar results, the EMD analyses suffer some problems derived from the mode mixing in most of the Intrinsic Mode Functions (IMFs).

A novel adaptive harmonic fractional Fourier transform is proposed for analysis of voiced speech signals. It provides a higher concentration than the short time Fourier transform (STFT) and avoids the cross interference components produced by the Wigner-Ville distribution and other bilinear representations. The proposed method rotates the base tone and harmonics in time-frequency domain. After the rotation, base tone and harmonics become in parallel to the time axis in time-frequency domain so that a high concentration can be achieved.

Personal identification based on radar gait measurement is an important application of biometric technology because it enables remote and continuous identification of people, irrespective of the lighting conditions and subjects' outfits. This study explores an effective time-velocity distribution and its relevant parameters for Doppler-radar-based personal gait identification using deep learning. Most conventional studies on radar-based gait identification used a short-time Fourier transform (STFT), which is a general method to obtain time-velocity distribution for motion recognition using Doppler radar. However, the length of the window function that controls the time and velocity resolutions of the time-velocity image was empirically selected, and several other methods for calculating high-resolution time-velocity distributions were not considered. In this study, we compared four types of representative time-velocity distributions calculated from the Doppler-radar-received signals: STFT, wavelet transform, Wigner-Ville distribution, and smoothed pseudo-Wigner-Ville distribution. In addition, the identification accuracies of various parameter settings were also investigated. We observed that the optimally tuned STFT outperformed other high-resolution distributions, and a short length of the window function in the STFT process led to a reasonable accuracy; the best identification accuracy was 99% for the identification of twenty-five test subjects. These results indicate that STFT is the optimal time-velocity distribution for gait-based personal identification using the Doppler radar, although the time and velocity resolutions of the other methods were better than those of the STFT.