scholarly journals Time Frequency analysis of Non-Stationary signals by Differential frequency window S –Transform

2018 ◽  
Vol 7 (2.7) ◽  
pp. 878
Author(s):  
B Murali Krishna ◽  
M Srinivas ◽  
S Raja Gopal ◽  
G L. P. Ashok
Keyword(s):  
Gaussian Function ◽  
Signal Amplitude ◽  
Frequency Resolution ◽  
Energy Localization ◽  
Major Function ◽  
Time Frequency ◽  
S Transform ◽  
Stationary Signals ◽  
Frequency Window ◽  
Non Stationary Signal

The S transform is an extension of Short Time Fourier Transform and Wavelet transform, has a time frequency resolution which is far from ideal. A differential frequency window is proposed in this paper to enhance the time frequency energy localization. When a non stationary signal consists of abrupt amplitude variation equal to peak of Gaussian function at initial intervals of chosen guassian window, then some part of the signal amplitude will be nullified during transform projection. The major function of differential frequency window is to track all abrupt amplitude-frequency variations which exploits in non – stationary signals. A mathematical method namely Newton Raphson method is adopted for this trace. The proposed scheme is tested for ECG data in presence of noise environment and results shows that proposed algorithm produces better enhanced energy localization in comparison to the standard S – Transform, STFT, and CWT. Furthermore the above algorithm is implemented on FPGA for real time applications.  

scholarly journals A Study of Parameters Setting of the STADZT

10.14311/1654 ◽  
2012 ◽  
Vol 52 (5) ◽  
Author(s):  
Václav Turoň
Keyword(s):  
Spectral Analysis ◽  
Fourier Transform ◽  
Frequency Resolution ◽  
Short Time Fourier Transform ◽  
Time Frequency ◽  
Stationary Signals ◽  
Zolotarev Polynomials ◽  
Non Stationary Signal ◽  
Short Time ◽  
Main Influence

This paper deals with the new time-frequency Short-Time Approximated Discrete Zolotarev Transform (STADZT), which is based on symmetrical Zolotarev polynomials. Due to the special properties of these polynomials, STADZT can be used for spectral analysis of stationary and non-stationary signals with the better time and frequency resolution than the widely used Short-Time Fourier Transform (STFT). This paper describes the parameters of STADZT that have the main influence on its properties and behaviour. The selected parameters include the shape and length of the segmentation window, and the segmentation overlap. Because STADZT is very similar to STFT, the paper includes a comparison of the spectral analysis of a non-stationary signal created by STADZT and by STFT with various settings of the parameters.

Power System Events Classification using Pattern Recognition Approach

2006 ◽  
Vol 6 (1) ◽  
Author(s):  
S. R. Samantaray ◽  
P. K. Dash ◽  
G. Panda
Keyword(s):  
Pattern Recognition ◽  
Power System ◽  
Accurate Method ◽  
Frequency Resolution ◽  
New Approach ◽  
Time Frequency ◽  
Absolute Phase ◽  
S Transform ◽  
S Matrix ◽  
Stationary Signals

A new approach for power system event recognition and classification using HS-transform and RBFNN is presented in this paper. Different power system events (disturbances) like sag, swell, notch, spike, transient, and chirp are generated and processed through Hyperbolic S-transform (HS-Transform). The excellent time-frequency resolution property of HS-Transform is used to extract useful information (features) from the non-stationary signals for pattern recognition. Here HS-transform generates the S-matrix and S-matrix provides the time-frequency contours, phase contours and absolute phase of the corresponding signal. From the above extracted information, various numerical indices like standard deviation, variance, norm, energy are found out. Further these indices are used as inputs to the Radial Basis Function Neural Network (RBFNN) for classifying different power system events accordingly. The RBFNN provides accurate results even with inputs (indices) found out under high noise conditions (SNR 20 dB). Thus the proposed method provides a robust and accurate method for power system events classification.

scholarly journals Time-Frequency Feature Analysis

2021 ◽  
Author(s):  
Behnaz Ghoraani
Keyword(s):  
Pattern Recognition ◽  
Real World ◽  
Feature Detection ◽  
Classification Systems ◽  
Time Frequency ◽  
Analysis Methodology ◽  
Stationary Signals ◽  
Time Varying Frequency ◽  
Non Stationary Signal ◽  
Discriminative Pattern

Most of the real-world signals in nature are non-stationary, i.e., their statistics are time variant. Extracting the time-varying frequency characteristics of a signal is very important in understanding the signal better, which could be of immense use in various applications such as pattern recognition and automated-decision making systems. In order to extract meaningful time-frequency (TF) features, a joint TF analysis is required. The proposed work is an attempt to develop a generalized TF analysis methodology that exploits the benefits of TF distribution (TFD) in pattern classification systems as related to discriminant feature detection and classification. Our objective is to introduce a unique and efficient way of performing non-stationary signal analysis using adaptive and discriminant TF techniques. To fulfill this objective, in the first point, we build a novel TF matrix (TFM) decomposition that increases the effectiveness of segmentation in real-world signals. Instantaneous and unique features are extracted from each segment such that they successfully represent joint TF structure of the signal. In the second point, based on the above technique, two unique and novel discriminant TF analysis methods are proposed to perform an improved and discriminant feature selection of any non-stationary signals. The first approach is a new machine learning method that identifies the clusters of the discriminant features to compute the presence of the discriminative pattern in any given signal, and classify them accordingly. The second approach is a discriminant TFM (DTFM) framework, which is a combination of TFM decomposition and the discriminant clustering techniques. The developed DTFM analysis automatically identifies the differences between different classes as the distinguishing structure, and uses the identified structure to accurately classify and locate the discriminant structure in the signal. The theoretical properties of the proposed approaches pertaining to pattern recognition and detection are examined in this dissertation. The extracted TF features provide strong and successful characterization and classification of real and synthetic non-stationary signals. The proposed TF techniques facilitate the adaptation of TF quantification to any feature detection technique in automating the identification process of discriminatory TF features, and can find applications in many different fields including biomedical and multimedia signal processing.

Machine Learning Classification of Cohen's Class Time-Frequency Representations of Non-Stationary Signals: Effects on Earthquake Detection

2021 ◽  
Author(s):  
Marko Njirjak ◽  
Erik Otović ◽  
Dario Jozinović ◽  
Jonatan Lerga ◽  
Goran Mauša ◽  
...  
Keyword(s):  
Machine Learning ◽  
Original Data ◽  
Stationary Time Series ◽  
Waveform Data ◽  
Time Frequency ◽  
Machine Learning Classification ◽  
Seismic Waveforms ◽  
Stationary Signals ◽  
Non Stationary Signal

<p>The analysis of non-stationary signals is often performed on raw waveform data or on Fourier transformations of those data, i.e., spectrograms. However, the possibility of alternative time-frequency representations being more informative than spectrograms or the original data remains unstudied. In this study, we tested if alternative time-frequency representations could be more informative for machine learning classification of seismic signals. This hypothesis was assessed by training three well-established convolutional neural networks, using nine different time-frequency representations, to classify seismic waveforms as earthquake or noise. The results were compared to the base model, which was trained on the raw waveform data. The signals used in the experiment were seismogram instances from the LEN-DB seismological dataset (Magrini et al. 2020). The results demonstrate that Pseudo Wigner-Ville and Wigner-Ville time-frequency representations yield significantly better results than the base model, while Margenau-Hill performs significantly worse (P < .01). Interestingly, the spectrogram, which is often used in non-stationary signal analysis, did not yield statistically significant improvements. This research could have a notable impact in the field of seismology because the data that were previously hidden in the seismic noise are now classified more accurately. Moreover, the results might suggest that alternative time-frequency representations could be used in other fields which use non-stationary time series to extract more valuable information from the original data. The potential fields encompass different fields of geophysics, speech recognition, EEG and ECG signals, gravitational waves and so on. This, however, requires further research.</p>

scholarly journals A Time–Frequency Correlation Analysis Method of Time Series Decomposition Derived from Synchrosqueezed S Transform

2019 ◽  
Vol 9 (4) ◽  
pp. 777 ◽  
Author(s):  
Gaoyuan Pan ◽  
Shunming Li ◽  
Yanqi Zhu
Keyword(s):  
Time Series ◽  
Correlation Analysis ◽  
Time Varying ◽  
Analysis Method ◽  
Frequency Correlation ◽  
Time Frequency ◽  
Time Series Decomposition ◽  
S Transform ◽  
Stationary Signals ◽  
Correlation Analysis Method

Traditional correlation analysis is analyzed separately in the time domain or the frequency domain, which cannot reflect the time-varying and frequency-varying characteristics of non-stationary signals. Therefore, a time–frequency (TF) correlation analysis method of time series decomposition (TD) derived from synchrosqueezed S transform (SSST) is proposed in this paper. First, the two-dimensional time–frequency matrices of the signals is obtained by synchrosqueezed S transform. Second, time series decomposition is used to transform the matrices into the two-dimensional time–time matrices. Third, a correlation analysis of the local time characteristics is carried out, thus attaining the time–frequency correlation between the signals. Finally, the proposed method is validated by stationary and non-stationary signals simulation and is compared with the traditional correlation analysis method. The simulation results show that the traditional method can obtain the overall correlation between the signals but cannot reflect the local time and frequency correlations. In particular, the correlations of non-stationary signals cannot be accurately identified. The proposed method not only obtains the overall correlations between the signals, but can also accurately identifies the correlations between non-stationary signals, thus showing the time-varying and frequency-varying correlation characteristics. The proposed method is applied to the acoustic signal processing of an engine–gearbox test bench. The results show that the proposed method can effectively identify the time–frequency correlation between the signals.

scholarly journals Classification in the Gabor time-frequency domain of non-stationary signals embedded in heavy noise with unknown statistical distribution

2010 ◽  
Vol 20 (1) ◽  
pp. 135-147 ◽  
Author(s):  
Ewa Świercz
Keyword(s):  
Pattern Recognition ◽  
Frequency Domain ◽  
Pattern Matching ◽  
Classification Algorithm ◽  
Statistical Distribution ◽  
Classification Rule ◽  
Matching Problem ◽  
Time Frequency ◽  
Stationary Signals ◽  
Non Stationary Signal

Classification in the Gabor time-frequency domain of non-stationary signals embedded in heavy noise with unknown statistical distributionA new supervised classification algorithm of a heavily distorted pattern (shape) obtained from noisy observations of nonstationary signals is proposed in the paper. Based on the Gabor transform of 1-D non-stationary signals, 2-D shapes of signals are formulated and the classification formula is developed using the pattern matching idea, which is the simplest case of a pattern recognition task. In the pattern matching problem, where a set of known patterns creates predefined classes, classification relies on assigning the examined pattern to one of the classes. Classical formulation of a Bayes decision rule requiresa prioriknowledge about statistical features characterising each class, which are rarely known in practice. In the proposed algorithm, the necessity of the statistical approach is avoided, especially since the probability distribution of noise is unknown. In the algorithm, the concept of discriminant functions, represented by Frobenius inner products, is used. The classification rule relies on the choice of the class corresponding to themaxdiscriminant function. Computer simulation results are given to demonstrate the effectiveness of the new classification algorithm. It is shown that the proposed approach is able to correctly classify signals which are embedded in noise with a very low SNR ratio. One of the goals here is to develop a pattern recognition algorithm as the best possible way to automatically make decisions. All simulations have been performed in Matlab. The proposed algorithm can be applied to non-stationary frequency modulated signal classification and non-stationary signal recognition.

Gaussian Window of Optimal Time-Frequency Resolution in Numerical Implementation of Short-Time Fourier Transform

2011 ◽  
Vol 48-49 ◽  
pp. 555-560 ◽  
Author(s):  
Yang Jin ◽  
Zhi Yong Hao
Keyword(s):  
Fourier Transform ◽  
Continuous Time ◽  
Gaussian Function ◽  
Frequency Resolution ◽  
Optimal Time ◽  
Numerical Implementation ◽  
Short Time Fourier Transform ◽  
Time Frequency ◽  
Gaussian Window ◽  
Short Time

In this paper, we report the condition to keep the optimal time-frequency resolution of the Gaussian window in the numerical implementation of the short-time Fourier transform. Because of truncation and discretization, the time-frequency resolution of the discrete Gaussian window is different from that of the proper Gaussian function. We compared the time-frequency resolution performance of the discrete Gaussian window and Hanning window based on that they have the same continuous-time domain standard deviation, and generalized the condition under which the time-frequency resolution of the Gaussian window will prevail over that of the Hanning window.

Harmonic Detection in Micro-Grid Based on Modified S-Transform

2014 ◽  
Vol 568-570 ◽  
pp. 270-273 ◽  
Author(s):  
Guan Qi Liu ◽  
Li Na Wu
Keyword(s):  
Harmonic Signal ◽  
Frequency Resolution ◽  
Harmonic Detection ◽  
New Approach ◽  
Time Frequency ◽  
Feature Vectors ◽  
S Transform ◽  
Attractive Candidate ◽  
Micro Grid ◽  
Grid Based

The excellent time–frequency resolution of the modified S-transform (MST) makes it an attractive candidate for analysis and detection of harmonic in micro-grid. This paper presents a new approach for micro-grid harmonic detection based on the MST. Firstly, the MST was performed for the harmonic signal, and then the feature vectors were extracted from the resulting time-frequency matrix. Finally, the frequency, amplitude and phase of the harmonic were obtained by analyzing and processing these feature vectors. Simulation results show that the proposed approach can detect the harmonic in micro-grid with high accuracy and strong noise immunity.

Investigation of generalized S-transform analysis windows for time-frequency analysis of seismic reflection data

Geophysics ◽  
2016 ◽  
Vol 81 (3) ◽  
pp. V235-V247 ◽  
Author(s):  
Duan Li ◽  
John Castagna ◽  
Gennady Goloshubin
Keyword(s):  
Temporal Resolution ◽  
Seismic Reflection ◽  
Frequency Resolution ◽  
Low Frequencies ◽  
Seismic Reflection Data ◽  
Time Frequency ◽  
Gaussian Window ◽  
Reflection Data ◽  
S Transform ◽  
Generalized S Transform

The frequency-dependent width of the Gaussian window function used in the S-transform may not be ideal for all applications. In particular, in seismic reflection prospecting, the temporal resolution of the resulting S-transform time-frequency spectrum at low frequencies may not be sufficient for certain seismic interpretation purposes. A simple parameterization of the generalized S-transform overcomes the drawback of poor temporal resolution at low frequencies inherent in the S-transform, at the necessary expense of reduced frequency resolution. This is accomplished by replacing the frequency variable in the Gaussian window with a linear function containing two coefficients that control resolution variation with frequency. The linear coefficients can be directly calculated by selecting desired temporal resolution at two frequencies. The resulting transform conserves energy and is readily invertible by an inverse Fourier transform. This modification of the S-transform, when applied to synthetic and real seismic data, exhibits improved temporal resolution relative to the S-transform and improved resolution control as compared with other generalized S-transform window functions.

scholarly journals S-Transform Based Analysis for Stock Market Volatility Estimation

2019 ◽  
Vol 8 (11) ◽  
pp. 3669-3675
Keyword(s):  
Financial Time Series ◽  
Theory And Practice ◽  
Frequency Resolution ◽  
Gaussian Kernel ◽  
Bench Mark ◽  
Data Sets ◽  
Stock Market Volatility ◽  
Asset Valuation ◽  
Time Frequency ◽  
S Transform

Financial Time series analysis (FTSA) is concerned with theory and practice of asset valuation over time. Generally, FTSA is useful for forecasting the asset volatility. This paper proposes the discrete S-Transform technique driven by Gaussian kernel for the estimation of volatility in FTSA. S-Transform is found to be a better tool in finding the time frequency resolution so as to predict and estimate the risk and returns of financial market. S-Transform prediction on two different bench mark data sets namely, Standard & Poor(S&P) 500 and Dow Jones Industrial Average(DJIA) index clearly indicates its superiority for the prediction of short and long-term trends in stock markets

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