Short-time Fourier transform and superoscillations

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.

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.

The primary objective of this paper is to develop output only modal identification and structural damage detection. Identification of multi-degree of freedom (MDOF) linear time invariant (LTI) and linear time variant (LTV—due to damage) systems based on Time-frequency (TF) techniques—such as short-time Fourier transform (STFT), empirical mode decomposition (EMD), and wavelets—is proposed. STFT, EMD, and wavelet methods developed to date are reviewed in detail. In addition a Hilbert transform (HT) approach to determine frequency and damping is also presented. In this paper, STFT, EMD, HT and wavelet techniques are developed for decomposition of free vibration response of MDOF systems into their modal components. Once the modal components are obtained, each one is processed using Hilbert transform to obtain the modal frequency and damping ratios. In addition, the ratio of modal components at different degrees of freedom facilitate determination of mode shape. In cases with output only modal identification using ambient/random response, the random decrement technique is used to obtain free vibration response. The advantage of TF techniques is that they are signal based; hence, can be used for output only modal identification. A three degree of freedom 1:10 scale model test structure is used to validate the proposed output only modal identification techniques based on STFT, EMD, HT, wavelets. Both measured free vibration and forced vibration (white noise) response are considered. The secondary objective of this paper is to show the relative ease with which the TF techniques can be used for modal identification and their potential for real world applications where output only identification is essential. Recorded ambient vibration data processed using techniques such as the random decrement technique can be used to obtain the free vibration response, so that further processing using TF based modal identification can be performed.

This paper presents the methodology, properties and processing of the time-frequency techniques for non-stationary signals, which are frequently used in biomedical, communication and image processing fields. Two classes of time-frequency analysis techniques are chosen for this study. One is short-time Fourier Transform (STFT) technique from linear time-frequency analysis and the other is the Wigner-Ville Distribution (WVD) from Quadratic time-frequency analysis technique. Algorithms for both these techniques are developed and implemented on non-stationary signals for spectrum analysis. The results of this study revealed that the WVD and its classes are most suitable for time-frequency analysis.

Doppler signals from a disturbed arterial blood flow are very likely to be nonstationary for they usually have a time-varying frequency structure caused by a complicated flow pattern. Therefore conventional Fourier analysis based methods are unsuitable for this application. This paper introduces the application of joint time-frequency analysis (TFA) to estimate the frequency dynamics of arterial Doppler blood flow signals and to detect the presence of small stenoses of the artery. The short time Fourier transform (STFT), Wigner distribution (WD), and Choi-Williams distribution (CWD) were investigated. The results of synthetic signal analysis show that the STFT, WD and CWD follow the transient changes of frequency well, and the STFT and CWD also behave well for multicomponent signals. Doppler spectra were obtained by means of the FFT, STFT, WD, and CWD for different flow rates and positions along a simulated blood vessel for stenoses ranging from 2% to 25% cross sectional area reduction (CSAR) using a blood analogue. The results indicate that all of these methods are to some extent capable of detecting stenoses as small as 2% CSAR by identifying the existence of negative frequency components in the spectra, and the CWD appears at this stage to be superior to the STFT and WD.

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).

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.

Narrow-band interference (NBI) is a critical issue for synthetic aperture radar (SAR), in which the imaging quality can be degraded severely. To suppress NBI effectively, a novel interference suppression algorithm using robust principal component analysis (RPCA) based signal separation in time-frequency domain is proposed. The RPCA algorithm is introduced for signal separation in the time-frequency domain for the first time. The fundamental assumption of RPCA is that a matrix can be modeled as a combination of a low-rank matrix and a sparse counterpart. In terms of the SAR echo, the short time Fourier transformation (STFT) matrix of mixed signals (i.e., useful SAR signals and NBIs) well fits the assumption of RPCA. Based on this property, radar echoes are first transformed into the time-frequency domain by STFT to form an STFT matrix. Then, the RPCA algorithm is used to decompose the STFT matrix into a low-rank matrix (i.e., NBIs) and a sparse matrix (i.e., useful signals). Finally, the NBIs can be reconstructed and subtracted from the echoes to realize the interference suppression. The experimental results of simulated and measured data demonstrate that the proposed algorithm not only can suppress interference effectively, but also preserve the useful information as much as possible.

As an important feature for micro-motion targets, micro-Doppler is widely used in parameters estimation and target classification. Aiming at the extraction of micro-Doppler, a method based on STFT (Short Time Fourier Transform, STFT) and RANSAC (Random Sample Consensus, RANSAC) is proposed. Firstly, the precession model of coneshaped target is established, and the parameterized expression of micro-Doppler is derived. Secondly, STFT is conducted on the echo to analyze the characteristic in time-frequency domain, and time-frequency maxima is used to acquire the time-frequency points set. Then, according to the parameterized expression, the prescribed fitting function is designed, and RANSAC is adopted to distinguish the valid micro-Doppler frequency points and the invalid points, and thus the micro-Doppler is estimated. Finally, the effectiveness of the proposed method is verified by experiments.

It is necessary to have both time and frequency domain information from measured acoustic signals of internal combustion engine (ICE) for noise, vibration and harshness (NVH) performance improvement and evaluation. This paper focuses on the time-frequency representation (TFR) of acoustic signals and the study of engine induction noise characteristics. The time-frequency analysis techniques, like the short-time Fourier transform (STFT) and continuous wavelet transform (WT), are reviewed in this paper. It shows that the engine induction noise is typical of non-stationary and the time-frequency method is significant to reveal the temporal localization of the signal's spectral components and to predict the engine physical phenomena. The TFR of the induction noise signal with STFT and CWT and the time-frequency characteristics are shown in this paper.

Chirp pulse compression technique can improve signal-to noise ratio of ultrasonic flaw signals. But its disadvantage is the presence of sidelobes which might mask nearby small flaws and make it difficult to separate multiple flaws. In this paper, time-frequency analysis (t-f analysis) is applied to ultrasonic chirp pulse compression signals for range resolution improvement. Short Time Fourier Transform (STFT) is adopted for t-f analysis, followed by the application of Minimization and Polarity Thresholding Algorithm to suppress the sidelobe. In order to achieve the low sidelobe level without suppressing the mainlobe, the STFT is calculated by varying the window length with frequency and both pseudo-twofold and pseudo fourfold frequency cos components obtained from the STFT are utilized. The method is applied to both simulated and measured ultrasonic flaw signals of chirp. The results show a good suppression of sidelobes and a further compression of pulse width with preserving both the polarity and the amplitude of signals.

Motivated by the human auditory system, a new signal transform is presented which models the way humans hear. Cochlear processing acts like a constant bandwidth bank of filters in the low frequency range but is of proportional bandwidth at higher frequencies. This new transform, which we call the composite wavelet transform, is better able to model this process than standard signal processing techniques such as the short‐time Fourier transform (STFT) and the continuous wavelet transform (CWT). The composite wavelet transform in fact provides a signal analysis tool that is able to examine signals with competing signal structures whereas the STFT and the CWT do not. In order to insure stable signal recovery, the theory of frames is examined. An overview of the theory of frames will be given and wavelet and Gabor frames will be discussed. Recent work on frames for the composite wavelet transform will also be presented. Finally, some applications of frames, especially to speech signal processing will be considered.

Freezing of Gait (FOG) is an impairment that affects the majority of patients in the advanced stages of Parkinson’s Disease (PD). FOG can lead to sudden falls and injuries, negatively impacting the quality of life for the patients and their families. Rhythmic Auditory Stimulation (RAS) can be used to help patients recover from FOG and resume normal gait. RAS might be ineffective due to the latency between the start of a FOG event, its detection and initialization of RAS. We propose a system capable of both FOG prediction and detection using signals from tri-axial accelerometer sensors that will be useful in initializing RAS with minimal latency. We compared the performance of several time frequency analysis techniques, including moving windows extracted from the signals, handcrafted features, Recurrence Plots (RP), Short Time Fourier Transform (STFT), Discreet Wavelet Transform (DWT) and Pseudo Wigner Ville Distribution (PWVD) with Deep Learning (DL) based Long Short Term Memory (LSTM) and Convolutional Neural Networks (CNN). We also propose three Ensemble Network Architectures that combine all the time frequency representations and DL architectures. Experimental results show that our ensemble architectures significantly improve the performance compared with existing techniques. We also present the results of applying our method trained on a publicly available dataset to data collected from patients using wearable sensors in collaboration with A.T. Still University.

We use recursive short-time Fourier transforms (STFT) for interference excision in PN spread spectrum communication systems. The proposed excision method is based on the attractive localization properties of the impulse responses of the multiple pole filters. These impulse responses have Gaussian-like shapes and decrease in bandwidth with higher pole multiplicities. When used as a data window before Fourier transformation, they result in a large class of computationally efficient STFTs. Localization measures can be applied to determine the proper window (impulse response), which maximally concentrates the jammer in the time-frequency domain. Interference mitigation is then achieved by applying a binary excision to the STFT employing the optimum window for each data bit. We show that this method permits both data-dependent windowing and filtering, and leads to improved BER performance of the DS/SS system.

This paper presents a motor imagery based Brain Computer Interface (BCI) that uses single channel EEG signal from the C3 or C4 electrode placed in the motor area of the head. Time frequency analysis using Short Time Fourier Transform (STFT) is used to compute spectrogram from the EEG data. The STFT is scaled to have gray level values on which Grey Co-occurrence Matrix (GLCM) is computed. Texture descriptors such as correlation, energy, contrast, homogeneity and dissimilarity are calculated from the GLCM matrices. The texture descriptors are used to train a logistic regression classifier which is then used to classify the left and right motor imagery signals. The single-channel motor imagery classification system is tested offline with different subjects. The average offline accuracy is 87.6%. An online BCI system is implemented in openViBE with the single channel classification scheme. The stimuli presentations and feedback are implemented in Python and integrated with the openViBe BCI system.