REDUNDANT MORPHOLOGICAL WAVELET AND LOCAL PATTERN SPECTRUM

2013 ◽  
Vol 11 (04) ◽  
pp. 1360001
Author(s):  
TOMONARI YAMAGUCHI ◽  
MITSUHIKO FUJIO ◽  
KATSUHIRO INOUE
Keyword(s):  
Wavelet Analysis ◽  
Discrete Wavelet ◽  
Short Time Fourier Transform ◽  
Shape Information ◽  
Local Pattern ◽  
Pattern Spectrum ◽  
Time Frequency ◽  
Stationary Signals ◽  
Shift Invariance ◽  
Short Time

Time-frequency analysis methods such as wavelet analysis are applied to investigate characteristic from non-stationary signals. In this study, we proposed redundant morphological wavelet analysis that was a kind of nonlinear discrete wavelet and redundant wavelet. This method analyzes a transition of shape information from signals in detail since this method keeps property of shift invariance though information of decomposition includes redundancy. Local pattern spectrum which corresponds to nonlinear short time Fourier transform is derived from this nonlinear wavelet. The characteristics of these methods were confirmed by applying to simulation data and actual data.

scholarly journals Joint Time-Frequency And Wavelet Analysis - An Introduction

2014 ◽  
Vol 21 (4) ◽  
pp. 741-758 ◽  
Author(s):  
Andrzej Majkowski ◽  
Marcin Kołodziej ◽  
Remigiusz J. Rak
Keyword(s):  
Wavelet Analysis ◽  
Frequency Analysis ◽  
Fourier Spectrum ◽  
Frequency Content ◽  
Short Time Fourier Transform ◽  
Time Frequency Analysis ◽  
Time Frequency ◽  
Stationary Signals ◽  
Frequency Window ◽  
Short Time

Abstract A traditional frequency analysis is not appropriate for observation of properties of non-stationary signals. This stems from the fact that the time resolution is not defined in the Fourier spectrum. Thus, there is a need for methods implementing joint time-frequency analysis (t/f) algorithms. Practical aspects of some representative methods of time-frequency analysis, including Short Time Fourier Transform, Gabor Transform, Wigner-Ville Transform and Cone-Shaped Transform are described in this paper. Unfortunately, there is no correlation between the width of the time-frequency window and its frequency content in the t/f analysis. This property is not valid in the case of a wavelet transform. A wavelet is a wave-like oscillation, which forms its own “wavelet window”. Compression of the wavelet narrows the window, and vice versa. Individual wavelet functions are well localized in time and simultaneously in scale (the equivalent of frequency). The wavelet analysis owes its effectiveness to the pyramid algorithm described by Mallat, which enables fast decomposition of a signal into wavelet components.

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.

scholarly journals Representation and Denoising of ECG Signal Using Hybrid Filtering Approach

2021 ◽  
Vol 9 (VII) ◽  
pp. 3281-3286
Author(s):  
Neeraj Venkat
Keyword(s):  
Feature Extraction ◽  
External Electromagnetic Field ◽  
Health Condition ◽  
Discrete Wavelet ◽  
Ecg Signal ◽  
Time Frequency ◽  
Interference Noise ◽  
Frequency Representation ◽  
Stationary Signals ◽  
Short Time

Electrocardiogram (ECG) signal plays an imperative role in monitoring and examining the health condition of the heart. ECG signal represents the electrical activity of the heat. The most consequential noises that degrade important features in ECG signal are powerline interference noise, external electromagnetic field interference noise, baseline wandering and electroencephalogram noise. The features of ECG signal obtained in time domain is not sufficient for analyzing the ECG signal. As the signal is non-stationary, the time-frequency representation can be used for feature extraction. The Short Time Fourier Transform can be used but its time frequency precision is not optimal. In this current project, we will be able to implement the ideology proposed to overcome the problem among various time frequency transformation. The discrete wavelet transform (DWT) is used which gives effective results for non-stationary signals like ECG signal which may be often contaminated. The combination of Savitzky-Golay filtering and DWT can be used for ECG denoising and feature extraction which has the advantage of preserving the important feature by elimination the noise components. The method is applied for the database which is taken from MIT- BIH arrhythmia and the algorithm is implemented in MATLAB platform.

scholarly journals Wavelets for EEG Analysis

2020 ◽  
Author(s):  
Nikesh Bajaj
Keyword(s):  
Wavelet Transform ◽  
Wavelet Analysis ◽  
Wavelet Packet ◽  
Discrete Wavelet ◽  
Eeg Signal ◽  
Time Frequency ◽  
Analysis Technique ◽  
Artefact Removal ◽  
Short Time ◽  
Electroencephalogram Eeg

This chapter introduces the applications of wavelet for Electroencephalogram (EEG) signal analysis. First, the overview of EEG signal is discussed to the recording of raw EEG and widely used frequency bands in EEG studies. The chapter then progresses to discuss the common artefacts that contaminate EEG signal while recording. With a short overview of wavelet analysis techniques, namely; Continues Wavelet Transform (CWT), Discrete Wavelet Transform (DWT), and Wavelet Packet Decomposition (WPD), the chapter demonstrates the richness of CWT over conventional time-frequency analysis technique e.g. Short-Time Fourier Transform. Lastly, artefact removal algorithms based on Independent Component Analysis (ICA) and wavelet are discussed and a comparative analysis is demonstrated. The techniques covered in this chapter show that wavelet analysis is well-suited for EEG signals for describing time-localised event. Due to similar nature, wavelet analysis is also suitable for other biomedical signals such as Electrocardiogram and Electromyogram.

scholarly journals Area-Efficient Short-Time Fourier Transform Processor for Time–Frequency Analysis of Non-Stationary Signals

2020 ◽  
Vol 10 (20) ◽  
pp. 7208
Author(s):  
Hohyub Jeon ◽  
Yongchul Jung ◽  
Seongjoo Lee ◽  
Yunho Jung
Keyword(s):  
Fourier Transform ◽  
Real Time ◽  
Frequency Analysis ◽  
Path Delay ◽  
Window Length ◽  
Short Time Fourier Transform ◽  
Time Frequency Analysis ◽  
Time Frequency ◽  
Stationary Signals ◽  
Short Time

In this paper, we propose an area-efficient short-time Fourier transform (STFT) processor that can perform time–frequency analysis of non-stationary signals in real time, which is essential for voice or radar-signal processing systems. STFT processors consist of a windowing module and a fast Fourier transform processor. The length of the window function is related to the time–frequency resolution, and the required window length varies depending on the application. In addition, the window function needs to overlap the input data samples to minimize the data loss in the window boundary, and overlap ratios of 25%, 50%, and 75% are generally used. Therefore, the STFT processor should ideally support a variable window length and overlap ratio and be implemented with an efficient hardware architecture for real-time time–frequency analysis. The proposed STFT processor is based on the radix-4 multi-path delay commutator (R4MDC) pipeline architecture and supports a variable length of 16, 64, 256, and 1024 and overlap ratios of 25%, 50%, and 75%. Moreover, the proposed STFT processor can be implemented with very low complexity by having a relatively lower number of delay elements, which are the ones that increase complexity in the most STFT processors. The proposed STFT processor was designed using hardware description language (HDL) and synthesized to gate-level circuits using a standard cell library in a 65 nm CMOS process. The proposed STFT processor results in logic gates of 197,970, which is 63% less than that of the conventional radix-2 single-path delay feedback (R2SDF) based STFT processor.

scholarly journals Strain Sensitivity Enhancement of Broadband Ultrasonic Signals in Plates Using Spectral Phase Filtering

2021 ◽  
Vol 11 (6) ◽  
pp. 2582
Author(s):  
Lucas M. Martinho ◽  
Alan C. Kubrusly ◽  
Nicolás Pérez ◽  
Jean Pierre von der Weid
Keyword(s):  
Fourier Transform ◽  
Guided Waves ◽  
Strain Level ◽  
Energy Concentration ◽  
Short Time Fourier Transform ◽  
Time Frequency ◽  
Frequency Representation ◽  
The Fourier Transform ◽  
Short Time ◽  
Sensitivity Gain

The focused signal obtained by the time-reversal or the cross-correlation techniques of ultrasonic guided waves in plates changes when the medium is subject to strain, which can be used to monitor the medium strain level. In this paper, the sensitivity to strain of cross-correlated signals is enhanced by a post-processing filtering procedure aiming to preserve only strain-sensitive spectrum components. Two different strategies were adopted, based on the phase of either the Fourier transform or the short-time Fourier transform. Both use prior knowledge of the system impulse response at some strain level. The technique was evaluated in an aluminum plate, effectively providing up to twice higher sensitivity to strain. The sensitivity increase depends on a phase threshold parameter used in the filtering process. Its performance was assessed based on the sensitivity gain, the loss of energy concentration capability, and the value of the foreknown strain. Signals synthesized with the time–frequency representation, through the short-time Fourier transform, provided a better tradeoff between sensitivity gain and loss of energy concentration.

scholarly journals Ultrasonic Assessment of Thickness and Bonding Quality of Coating Layer Based on Short-Time Fourier Transform and Convolutional Neural Networks

Coatings ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 909
Author(s):  
Azamatjon Kakhramon ugli Malikov ◽  
Younho Cho ◽  
Young H. Kim ◽  
Jeongnam Kim ◽  
Junpil Park ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Coating Layer ◽  
Ultrasonic Pulse ◽  
Short Time Fourier Transform ◽  
Coating Materials ◽  
Time Frequency ◽  
High Attenuation ◽  
Bonding State ◽  
The Time Domain ◽  
Short Time

Ultrasonic non-destructive analysis is a promising and effective method for the inspection of protective coating materials. Offshore coating exhibits a high attenuation rate of ultrasonic energy due to the absorption and ultrasonic pulse echo testing becomes difficult due to the small amplitude of the second echo from the back wall of the coating layer. In order to address these problems, an advanced ultrasonic signal analysis has been proposed. An ultrasonic delay line was applied due to the high attenuation of the coating layer. A short-time Fourier transform (STFT) of the waveform was implemented to measure the thickness and state of bonding of coating materials. The thickness of the coating material was estimated by the projection of the STFT into the time-domain. The bonding and debonding of the coating layers were distinguished using the ratio of the STFT magnitude peaks of the two subsequent wave echoes. In addition, the advantage of the STFT-based approach is that it can accurately and quickly estimate the time of flight (TOF) of a signal even at low signal-to-noise ratios. Finally, a convolutional neural network (CNN) was applied to automatically determine the bonding state of the coatings. The time–frequency representation of the waveform was used as the input to the CNN. The experimental results demonstrated that the proposed method automatically determines the bonding state of the coatings with high accuracy. The present approach is more efficient compared to the method of estimating bonding state using attenuation.

scholarly journals A combined generalized Warblet transform and second order synchroextracting transform for analyzing nonstationary signals of rotating machinery

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Kai Wei ◽  
Xuwen Jing ◽  
Bingqiang Li ◽  
Chao Kang ◽  
Zhenhuan Dou ◽  
...  
Keyword(s):  
Vibration Signal ◽  
Rotating Machinery ◽  
Second Order ◽  
Variable Speed ◽  
Short Time Fourier Transform ◽  
Stationary Characteristic ◽  
Nonstationary Signals ◽  
Time Frequency ◽  
Effective Technology ◽  
Short Time

AbstractIn recent years, considerable attention has been paid in time–frequency analysis (TFA) methods, which is an effective technology in processing the vibration signal of rotating machinery. However, TFA techniques are not sufficient to handle signals having a strong non-stationary characteristic. To overcome this drawback, taking short-time Fourier transform as a link, a TFA methods that using the generalized Warblet transform (GWT) in combination with the second order synchroextracting transform (SSET) is proposed in this study. Firstly, based on the GWT and SSET theories, this paper proposes a method combining the two TFA methods to improve the TFA concentration, named GWT–SSET. Secondly, the method is verified numerically with single-component and multi-component signals, respectively. Quantized indicators, Rényi entropy and mean relative error (MRE) are used to analyze the concentration of TFA and accuracy of instantly frequency (IF) estimation, respectively. Finally, the proposed method is applied to analyze nonstationary signals in variable speed. The numerical and experimental results illustrate the effectiveness of the GWT–SSET method.

A Modified S-Transform for EEG Signals Analysis

2015 ◽  
Vol 12 (03) ◽  
pp. 1550021 ◽  
Author(s):  
M. A. Al-Manie ◽  
W. J. Wang
Keyword(s):  
Image Processing ◽  
Fourier Transform ◽  
Energy Concentration ◽  
Biomedical Data ◽  
Short Time Fourier Transform ◽  
Phase Information ◽  
Eeg Signals ◽  
Time Frequency ◽  
S Transform ◽  
Short Time

Due to the advantages offered by the S-transform (ST) distribution, it has been recently successfully implemented for various applications such as seismic and image processing. The desirable properties of the ST include a globally referenced phase as the case with the short time Fourier transform (STFT) while offering a higher spectral resolution as the wavelet transform (WT). However, this estimator suffers from some inherent disadvantages seen as poor energy concentration with higher frequencies. In order to improve the performance of the distribution, a modification to the existing technique is proposed. Additional parameters are proposed to control the window's width which can greatly enhance the signal representation in the time–frequency plane. The new estimator's performance is evaluated using synthetic signals as well as biomedical data. The required features of the ST which include invertability and phase information are still preserved.

Variable Speed Estimation for Wheel-Bearings with STFT and BP Neural Network

2014 ◽  
Vol 945-949 ◽  
pp. 1112-1115
Author(s):  
Yuan Zhou ◽  
Bin Chen ◽  
Bao Cheng Gao ◽  
Si Jie Zhang
Keyword(s):  
Neural Network ◽  
Bp Neural Network ◽  
Background Noise ◽  
Speed Estimation ◽  
Variable Speed ◽  
Short Time Fourier Transform ◽  
Time Frequency ◽  
Novel Method ◽  
Instantaneous Frequencies ◽  
Short Time

For the variable speed estimation of wheel-bearings in strong background noise, a novel method with the short-time Fourier transform and BP neural network (STFT-BPNN) is proposed. In the method, it calculates the time-frequency spectrum with STFT technique. Then the instantaneous frequency is estimated by peak detection. Taking the instantaneous frequencies as the input vectors, the BP neural network is trained to fit the discrete instantaneous frequencies. The effectiveness of proposed method is demonstrated by simulation. Experimental results show that proposed method provides better performance on variable speed estimation for wheel-bearings.

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