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.

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 Time-Frequency Analysis of Compressor Rotating Stall by Means of Wavelet Transform

1996 ◽  
Author(s):  
Shengfang Liao ◽  
Jingyi Chen
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Wavelet Transform ◽  
Frequency Analysis ◽  
Rotating Stall ◽  
Processing Methods ◽  
Stall Inception ◽  
Time Frequency ◽  
Signal Processing Methods ◽  
Conventional Signal

In this paper, an application of Wavelet Transform, which is a newly developed time-frequency technique of signal processing, is demonstrated in analyzing compressor rotating stall signals. In contrast to conventional signal processing methods, e.g. Fourier Transform, Wavelet Transform is very suitable for analyzing transient processes as rotating stall inception in compressors. In this study, some typical rotating stall signals are processed via Morlet’s wavelet. It is concluded that Wavelet Transform has a great advantage in detecting rotating stall inceptions, which are usually very weak and embedded in relatively stronger noises. In the diagrams resulted from the transform, every emergence of precursor as well as full stall signals of a certain frequency is illustrated versus time.

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.

An Adaptive Time–Frequency Representation and its Fast Implementation

2006 ◽  
Vol 129 (2) ◽  
pp. 169-178 ◽  
Author(s):  
Bao Liu ◽  
Sherman Riemenschneider ◽  
Zuowei Shen
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Frequency Analysis ◽  
Continuous Wavelet Transform ◽  
Continuous Wavelet ◽  
Short Time Fourier Transform ◽  
Time Frequency ◽  
Frequency Representation ◽  
Adaptive Time ◽  
Short Time

This paper presents a fast adaptive time–frequency analysis method for dealing with the signals consisting of stationary components and transients, which are encountered very often in practice. It is developed based on the short-time Fourier transform but the window bandwidth varies along frequency adaptively. The method therefore behaves more like an adaptive continuous wavelet transform. We use B-splines as the window functions, which have near optimal time–frequency localization, and derive a fast algorithm for adaptive time–frequency representation. The method is applied to the analysis of vibration signals collected from rotating machines with incipient localized defects. The results show that it performs obviously better than the short-time Fourier transform, continuous wavelet transform, and several other most studied time–frequency analysis techniques for the given task.

scholarly journals Time-frequency analysis of the Surge Onset in the Centrifugal Blower

2015 ◽  
Vol 5 (1) ◽  
Author(s):  
Grzegorz Liskiewicz ◽  
Longin Horodko
Keyword(s):  
Wavelet Transform ◽  
Frequency Analysis ◽  
Continuous Wavelet Transform ◽  
Working Condition ◽  
Continuous Wavelet ◽  
Transient Phase ◽  
Centrifugal Blower ◽  
Time Frequency Analysis ◽  
Time Frequency ◽  
Pressure Signal

Abstract Time frequency analysis of the surge onset was performed in the centrifugal blower. A pressure signal was registered at the blower inlet, outlet and three locations at the impeller shroud. The time-frequency scalograms were obtained by means of the Continuous Wavelet Transform (CWT). The blower was found to successively operate in four different conditions: stable working condition, inlet recirculation, transient phase and deep surge. Scalograms revealed different spectral structures of aforementioned phases and suggest possible ways of detecting the surge predecessors.

Phase-based spectrum analysis method for identifying weak harmonics

2018 ◽  
Vol 24 (23) ◽  
pp. 5585-5596 ◽  
Author(s):  
Jingsong Xie ◽  
Wei Cheng ◽  
Yanyang Zi ◽  
Mingquan Zhang
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Wavelet Transform ◽  
Characteristic Frequency ◽  
Discrete Wavelet ◽  
Accurate Identification ◽  
Processing Methods ◽  
Characteristic Frequencies ◽  
Frequency Detection ◽  
Signal Processing Methods

Fault characteristic frequency extraction is an important means for the fault diagnosis of rotating machineries. Traditional signal processing methods commonly use the amplitude information of signals to detect damages. However, when the amplitudes of characteristic frequencies are weak, the recognition effects of traditional methods may be unsatisfactory. Therefore, this paper proposes the phase-based enhanced phase waterfall plot (EPWP) method and frequency equal ratio line (FERL) method for identifying weak harmonics. Taking a cracked rotor as an example, the characteristic frequency detection performances of the EPWP and FERL methods are compared with that of the traditional signal processing methods namely fast Fourier transform, short-time Fourier transform, discrete wavelet transform, continuous wavelet transform, ensemble empirical mode decomposition, and Hilbert–Huang transform. Research results demonstrate that the effects of EPWP and FERL for the recognitions of weak harmonics which are contained in steady signals and transient signals are better than that of the traditional signal processing methods. The accurate identification of weak characteristic frequencies in the vibration signals can provide an important reference for damage detections and improve the diagnostic accuracy.

Research on Goniometer Fault Detection of a Certain Missile Based on Wavelet Analysis

2012 ◽  
Vol 490-495 ◽  
pp. 1600-1604
Author(s):  
Zhu Lin Wang ◽  
Jiang Kun Mao ◽  
Zi Bin Zhang ◽  
Xi Wei Guo
Keyword(s):  
Wavelet Transform ◽  
Wavelet Analysis ◽  
Discrete Wavelet Transform ◽  
Frequency Analysis ◽  
Discrete Wavelet ◽  
Analysis Method ◽  
Frequency Method ◽  
Time Frequency Analysis ◽  
Time Frequency ◽  
Fault Characteristic

Aiming at the problem of existing time-frequency analysis methods was not effective to goniometer keeping fault of a certain missile, combined time -frequency analysis method of CWT and DWT for the fault was put forward based on the fault characteristic. The process of the method proposed was given and the time-frequency method of continuous and discrete wavelet transform was analysed. The signal when goniometer keeping fault occurred was analysed by the method that was put forward. The simulation showed that the method which was effective to the fault detecting could accurately detect the time and location of goniometer fault occurred.

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.

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