scholarly journals Comparative Application of Time-Frequency Methods on Strong Motion Signals

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Mohammad Ashtari Jafari
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Strong Motion ◽  
Energy Concentration ◽  
Signal Frequency ◽  
Discrete Wavelet ◽  
Continuous Wavelet ◽  
Frequency Content ◽  
Fourier Decomposition ◽  
Time Frequency

Real-world physical signals are commonly nonstationary, and their frequency details change with time and do not remain constant. Fourier transform that uses infinite sine/cosine waves as basis functions represents frequency constituents of signals but does not show the variations of the signal frequency contents over time. Multiresolution demonstration of the time-frequency domain may be achieved by the techniques that can support adjustable resolution in time and frequency. Earthquake strong motion signals are nonstationary and indicate time-varying frequency content due to the scattering from the source to the site. In this paper, we applied short-time Fourier transform, S-transform, continuous wavelet transform, fast discrete wavelet transform, synchrosqueezing transform, synchroextracting transform, continuous wavelet synchrosqueezing, filter bank synchrosqueezing, empirical mode decomposition, and Fourier decomposition methods on the near-source strong motion signals from the 7 May 2020 Mosha-Iran earthquake to study and compare the frequency content of this event estimated by these methods. According to the results that are examined by Renyi entropy and relative error, synchroextracting performed better in terms of energy concentration, and the Fourier decomposition method revealed the lowest difference between the original and reconstructed records.

scholarly journals Time Frequency Analysis of Wavelet and Fourier Transform

2020 ◽  
Author(s):  
Karlton Wirsing
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Wavelet Transform ◽  
Frequency Domain ◽  
Frequency Analysis ◽  
Discrete Wavelet ◽  
Continuous Wavelet ◽  
Time Frequency ◽  
Efficient Access ◽  
The Fourier Transform

Signal processing has long been dominated by the Fourier transform. However, there is an alternate transform that has gained popularity recently and that is the wavelet transform. The wavelet transform has a long history starting in 1910 when Alfred Haar created it as an alternative to the Fourier transform. In 1940 Norman Ricker created the first continuous wavelet and proposed the term wavelet. Work in the field has proceeded in fits and starts across many different disciplines, until the 1990’s when the discrete wavelet transform was developed by Ingrid Daubechies. While the Fourier transform creates a representation of the signal in the frequency domain, the wavelet transform creates a representation of the signal in both the time and frequency domain, thereby allowing efficient access of localized information about the signal.

Spectral decomposition of seismic data with continuous-wavelet transform

Geophysics ◽  
2005 ◽  
Vol 70 (6) ◽  
pp. P19-P25 ◽  
Author(s):  
Satish Sinha ◽  
Partha S. Routh ◽  
Phil D. Anno ◽  
John P. Castagna
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Time Scale ◽  
Fixed Time ◽  
Frequency Resolution ◽  
Continuous Wavelet ◽  
Window Length ◽  
Time Frequency ◽  
Frequency Map

This paper presents a new methodology for computing a time-frequency map for nonstationary signals using the continuous-wavelet transform (CWT). The conventional method of producing a time-frequency map using the short time Fourier transform (STFT) limits time-frequency resolution by a predefined window length. In contrast, the CWT method does not require preselecting a window length and does not have a fixed time-frequency resolution over the time-frequency space. CWT uses dilation and translation of a wavelet to produce a time-scale map. A single scale encompasses a frequency band and is inversely proportional to the time support of the dilated wavelet. Previous workers have converted a time-scale map into a time-frequency map by taking the center frequencies of each scale. We transform the time-scale map by taking the Fourier transform of the inverse CWT to produce a time-frequency map. Thus, a time-scale map is converted into a time-frequency map in which the amplitudes of individual frequencies rather than frequency bands are represented. We refer to such a map as the time-frequency CWT (TFCWT). We validate our approach with a nonstationary synthetic example and compare the results with the STFT and a typical CWT spectrum. Two field examples illustrate that the TFCWT potentially can be used to detect frequency shadows caused by hydrocarbons and to identify subtle stratigraphic features for reservoir characterization.

COMPLEMENTARY ANALYSIS TO HEART SOUNDS WHILE USING THE SHORT TIME FOURIER AND THE CONTINUOUS WAVELET TRANSFORMS

2007 ◽  
Vol 19 (05) ◽  
pp. 331-339
Author(s):  
S. M. Debbal ◽  
F. Bereksi-Reguig
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Wavelet Transforms ◽  
Continuous Wavelet ◽  
Short Time Fourier Transform ◽  
Continuous Wavelet Transforms ◽  
Time Frequency ◽  
Quantitative Measurements ◽  
Short Time

This paper presents the analysis and comparisons of the short time Fourier transform (STFT) and the continuous wavelet transform techniques (CWT) to the four sounds analysis (S1, S2, S3 and S4). It is found that the spectrogram short-time Fourier transform (STFT), cannot perfectly detect the internals components of these sounds that the continuous wavelet transform. However, the short time Fourier transform can provide correctly the extent of time and frequency of these four sounds. Thus, the STFT and the CWT techniques provide more features and characteristics of the sounds that will hemp physicians to obtain qualitative and quantitative measurements of the time-frequency characteristics.

THE FAST FOURIER TRANSFORM AND THE CONTINUOUS WAVELET TRANSFORM ANALYSIS OF THE PHONOCARDIOGRAM SIGNAL

2004 ◽  
Vol 04 (03) ◽  
pp. 257-272 ◽  
Author(s):  
S. M. DEBBAL ◽  
F. BEREKSI-REGUIG ◽  
A. MEZIANE TANI
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Fast Fourier Transform ◽  
Continuous Wavelet Transform ◽  
Continuous Wavelet ◽  
Time Frequency ◽  
Quantitative Measurements ◽  
Signal Characteristics ◽  
Wavelet Transform Analysis ◽  
Pcg Signals

This paper is concerned with a synthesis study of the fast Fourier transform (FFT) and the continuous wavelet transform (CWT) in analysing the phonocardiogram signal (PCG). It is shown that the continuous wavelet transform provides enough features of the PCG signals that will help clinics to obtain qualitative and quantitative measurements of the time-frequency PCG signal characteristics and consequently aid to diagnosis. Similary, it is shown that the frequency content of such a signal can be determined by the FFT without difficulties.

Constrained least-squares spectral analysis: Application to seismic data

Geophysics ◽  
2012 ◽  
Vol 77 (5) ◽  
pp. V143-V167 ◽  
Author(s):  
Charles I. Puryear ◽  
Oleg N. Portniaguine ◽  
Carlos M. Cobos ◽  
John P. Castagna
Keyword(s):  
Spectral Analysis ◽  
Fourier Transform ◽  
Wavelet Transform ◽  
Seismic Data ◽  
Continuous Wavelet ◽  
Window Length ◽  
Short Time Fourier Transform ◽  
Constrained Least Squares ◽  
Time Frequency ◽  
Short Time

An inversion-based algorithm for computing the time-frequency analysis of reflection seismograms using constrained least-squares spectral analysis is formulated and applied to modeled seismic waveforms and real seismic data. The Fourier series coefficients are computed as a function of time directly by inverting a basis of truncated sinusoidal kernels for a moving time window. The method resulted in spectra that have reduced window smearing for a given window length relative to the discrete Fourier transform irrespective of window shape, and a time-frequency analysis with a combination of time and frequency resolution that is superior to the short time Fourier transform and the continuous wavelet transform. The reduction in spectral smoothing enables better determination of the spectral characteristics of interfering reflections within a short window. The degree of resolution improvement relative to the short time Fourier transform increases as window length decreases. As compared with the continuous wavelet transform, the method has greatly improved temporal resolution, particularly at low frequencies.

scholarly journals An Approach on MCSA-Based Fault Detection Using Discrete Wavelet Transform and Fault Classification Based on Deep Neural Networks

2021 ◽  
Vol 10 (3) ◽  
pp. 2256-2259
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Fast Fourier Transform ◽  
Discrete Wavelet Transform ◽  
Three Dimensional ◽  
Fault Classification ◽  
Signal Frequency ◽  
Discrete Wavelet ◽  
Novel Approach ◽  
Motor Current Signature Analysis

This paper presents a novel approach on motor current signature analysis (MCSA) forbroken Rotor Bar fault and High Contact Resistance fault using stator current signals as an input from the three phases of Induction motors. Discrete Wavelet Transform is preferred over the Fast Fourier Transform (FFT). Fast Fourier Transform (FFT) converts signals from time domain to frequency domain on the other hand Discrete Wavelet Transform (DWT) gives complete three-dimensional information of the signal, frequency, amplitude, and the time where the frequency components exist. In wavelet analysis, thesignal is converted into scaled and translated version of mother wavelet, which is very irregular so cannot be predicted. Hence, mother wavelets are more appropriate for predicting the local behavior of the signal including irregularities and spikes. In this research features are extracted using DWT and then features are trained in Deep NN sequential model for the purpose of classification of the faults. In this research, MATLAB software has been used for building the motor model in Simulink environment and PyCharm software is used to implement Deep NN for getting accuracy and classification results. This research helps in early detection of the faults that assists in prevention from unscheduled downtimes in industry, economy loss and production loss as well.

scholarly journals Discrimination of Different AE and EMR Signals during Excavation of Coal Roadway Based on Wavelet Transform

Minerals ◽  
2022 ◽  
Vol 12 (1) ◽  
pp. 63
Author(s):  
Baolin Li ◽  
Zhonghui Li ◽  
Enyuan Wang ◽  
Nan Li ◽  
Jing Huang ◽  
...  
Keyword(s):  
Wavelet Transform ◽  
Rock Fracture ◽  
Discrete Wavelet ◽  
Continuous Wavelet ◽  
Time Frequency ◽  
Danger Signals ◽  
Long Period ◽  
Coal Roadway ◽  
Interference Signals ◽  
Precursor Information

During the process of coal road excavation, various interference signals, induced by environmental noise, drilling, and scraper loader, will affect the risk assessment of coal and gas outburst using acoustic emission (AE) and electromagnetic radiation (EMR) monitoring technology. To distinguish between different interference signals and danger signals, discrete wavelet transform (DWT) was used to decompose and reconstruct signals, and continuous wavelet transform (CWT) was used to obtain the time-frequency plane. The research results show that: (1) interference signals generally exhibit fluctuating changes within small ranges; in comparison, the intensity of AE and EMR signals caused by coal and rock fracture is found to continuously rise for a long period (longer than 2 h). (2) Different interference signals and danger signals differ significantly in their time-frequency plane. (3) Through decomposition and reconstruction of original signal, obvious precursor information can be found in the time-frequency plane of reconstructed signals.

scholarly journals Time-frequency analysis on gong timor music using short-time fourier transform and continuous wavelet transform

2017 ◽  
Vol 3 (3) ◽  
pp. 146
Author(s):  
Yovinia Carmeneja Hoar Siki ◽  
Natalia Magdalena Rafu Mamulak
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Frequency Analysis ◽  
Continuous Wavelet Transform ◽  
Continuous Wavelet ◽  
Short Time Fourier Transform ◽  
Time Frequency Analysis ◽  
Time Frequency ◽  
Music Signal ◽  
Short Time

Time-Frequency Analysis on Gong Timor Music has an important role in the application of signal-processing music such as tone tracking and music transcription or music signal notation. Some of Gong characters is heard by different ways of forcing Gong himself, such as how to play Gong based on the Player’s senses, a set of Gong, and by changing the tempo of Gong instruments. Gong's musical signals have more complex analytical criteria than Western music instrument analysis. This research uses a Gong instrument and two notations; frequency analysis of Gong music frequency compared by the Short-time Fourier Transform (STFT), Overlap Short-time Fourier Transform (OSTFT), and Continuous Wavelet Transform (CWT) method. In the STFT and OSTFT methods, time-frequency analysis Gong music is used with different windows and hop size while CWT method uses Morlet wavelet. The results show that the CWT is better than the STFT methods.

scholarly journals Energy-Period Profiles of Brain Networks in Group fMRI Resting-State Data: A Comparison of Empirical Mode Decomposition With the Short-Time Fourier Transform and the Discrete Wavelet Transform

2021 ◽  
Vol 15 ◽  
Author(s):  
Dietmar Cordes ◽  
Muhammad F. Kaleem ◽  
Zhengshi Yang ◽  
Xiaowei Zhuang ◽  
Tim Curran ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Resting State ◽  
Discrete Wavelet ◽  
Frequency Content ◽  
Resting State Networks ◽  
Short Time Fourier Transform ◽  
State Data ◽  
Mode Decomposition ◽  
Short Time

Traditionally, functional networks in resting-state data were investigated with linear Fourier and wavelet-related methods to characterize their frequency content by relying on pre-specified frequency bands. In this study, Empirical Mode Decomposition (EMD), an adaptive time-frequency method, is used to investigate the naturally occurring frequency bands of resting-state data obtained by Group Independent Component Analysis. Specifically, energy-period profiles of Intrinsic Mode Functions (IMFs) obtained by EMD are created and compared for different resting-state networks. These profiles have a characteristic distribution for many resting-state networks and are related to the frequency content of each network. A comparison with the linear Short-Time Fourier Transform (STFT) and the Maximal Overlap Discrete Wavelet Transform (MODWT) shows that EMD provides a more frequency-adaptive representation of different types of resting-state networks. Clustering of resting-state networks based on the energy-period profiles leads to clusters of resting-state networks that have a monotone relationship with frequency and energy. This relationship is strongest with EMD, intermediate with MODWT, and weakest with STFT. The identification of these relationships suggests that EMD has significant advantages in characterizing brain networks compared to STFT and MODWT. In a clinical application to early Parkinson’s disease (PD) vs. normal controls (NC), energy and period content were studied for several common resting-state networks. Compared to STFT and MODWT, EMD showed the largest differences in energy and period between PD and NC subjects. Using a support vector machine, EMD achieved the highest prediction accuracy in classifying NC and PD subjects among STFT, MODWT, and EMD.

Research on Applications of Wavelet Transform Threshold Method to Strong Motion Signal Processing

2012 ◽  
Vol 446-449 ◽  
pp. 2387-2391
Author(s):  
Wei Li ◽  
Shan You Li ◽  
Zhen Zhao ◽  
Zhi Xin Sun
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Wavelet Transform ◽  
High Frequency ◽  
Strong Motion ◽  
Short Time Fourier Transform ◽  
Threshold Method ◽  
Time Frequency ◽  
Motion Signal ◽  
Short Time

Fourier transform and short-time Fourier transform are the main methods in signal analysis, which can reflect the spectrum signature of signals in the whole time domain; but they cannot be used in the multi-resolution analysis on the non-stationary signals. However, the wavelet transform overcome the limits of Fourier and short-time Fourier transform, which can be performed in accurate time-frequency analysis of signals. Furthermore, the diversity of wavelet functions makes the wavelet transform more adaptive and flexible. Applying the wavelet transform to seismic signal processing is the complement and improvement of existing processing methods. In this paper, the basic theory of the wavelet threshold denoising method and its application to the strong motion signal processing were mainly introduced. The high-frequency noises were removed, and simultaneously the high-frequency signals were effectively retained.

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