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 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.

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.

scholarly journals Spectrogram analysis of selected tremor signals using short-time Fourier transform and continuous wavelet transform

1999 ◽  
Vol 42 (3) ◽  
Author(s):  
T. Bartosch ◽  
D. Seidl
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Time Varying ◽  
Continuous Wavelet ◽  
Short Time Fourier Transform ◽  
Array Data ◽  
Definition Of ◽  
Short Time

Among a variety of spectrogram methods Short-Time Fourier Transform (STFT) and Continuous Wavelet Transform (CWT) were selected to analyse transients in non-stationary tremor signals. Depending on the properties of the tremor signal a more suitable representation of the signal is gained by CWT. Three selected broadband tremor signals from the volcanos Mt. Stromboli, Mt. Semeru and Mt. Pinatubo were analyzed using both methods. The CWT can also be used to extend the definition of coherency into a time-varying coherency spectrogram. An example is given using array data from the volcano Mt. Stromboli.

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 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.

Sign in / Sign up

Export Citation Format

Share Document