The Uncertainty Principle for the Short-Time Fourier Transform and Wavelet Transform

2001 ◽  
pp. 217-232 ◽  
Author(s):  
Leon Cohen
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Uncertainty Principle ◽  
Short Time Fourier Transform ◽  
Short Time

Identification of Static Unbalance Wheel of Passenger Car Carried out on a Road

2014 ◽  
Vol 214 ◽  
pp. 48-57 ◽  
Author(s):  
Krzysztof Prażnowski ◽  
Sebastian Brol ◽  
Andrzej Augustynowicz
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Constant Velocity ◽  
Fourier Transforms ◽  
Static Condition ◽  
Rotational Frequency ◽  
Acceleration Sensor ◽  
Short Time Fourier Transform ◽  
Road Roughness ◽  
Short Time

This paper presents a method of identification of non-homogeneity or static unbalance of the structure of a car wheel based on a simple road test. In particular a method the detection of single wheel unbalance is proposed which applies an acceleration sensor fixed on windscreen. It measures accelerations cause by wheel unbalance among other parameters. The location of the sensor is convenient for handling an autonomous device used for diagnostic purposes. Unfortunately, its mounting point is located away from wheels. Moreover, the unbalance forces created by wheels spin are dumped by suspension elements as well as the chassis itself. It indicates that unbalance acceleration will be weak in comparison to other signals coming from engine vibrations, road roughness and environmental effects. Therefore, the static unbalance detection in the standard way is considered problematic and difficult. The goal of the undertaken research is to select appropriate transformations and procedures in order to determine wheel unbalance in these conditions. In this investigation regular and short time Fourier transform were used as well as wavelet transform. It was found that the use of Fourier transforms is appropriate for static condition (constant velocity) but the results proves that the wavelet transform is more suitable for diagnostic purposes because of its ability of producing clearer output even if car is in the state of acceleration or deceleration. Moreover it was proved that in the acceleration spectrum of acceleration measured on the windscreen a significant peak can be found when car runs with an unbalanced wheel. Moreover its frequency depends on wheel rotational frequency. For that reason the diagnostic of single wheel unbalance can be made by applying this method.

scholarly journals Application of Short Time Fourier Transform and Wavelet Transform for Sound Source Localization Using Single Moving Microphone in Machine Condition Monitoring

2016 ◽  
Vol 1 (1) ◽  
Author(s):  
Meifal Rusli
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Sound Source ◽  
Low Frequency ◽  
Peak Position ◽  
Source Position ◽  
Short Time Fourier Transform ◽  
Sound Sources ◽  
Time Frequency ◽  
Short Time

<p class="TTPParagraphothers"><em>The paper discusses means to predict sound source position emitted by fault machine components based on a single microphone moving in a linear track with constant speed.</em> The position of sound source that consists of some frequency spectrum is detected by time-frequency distribution of the sound signal through Short Time Fourier Transform (STFT) and Continues Wavelet Transform (CWT). <em>As the amplitude of sound pressure increases when the microphone moves closer, the source position and frequency are predicted from the peaks of time-frequency contour map</em><em>. </em>Firstly, numerical simulation is conducted using two sound sources that generate four different frequencies of sound. The second case is experimental analysis using rotating machine being monitored with unbalanced, misalignment and bearing defect. The result shows that application of both STFT and CWT are able to detect multiple sound sources position with multiple frequency peaks caused by machine fault. The STFT can indicate the frequency very clearly, but not for the peak position. On the other hand, the CWT is able to predict the position of sound at low frequency very clearly. However, it is failed to detect the exact frequency because of overlapping.</p>

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.

Frequency‐time decomposition of seismic data using wavelet‐based methods

Geophysics ◽  
1995 ◽  
Vol 60 (6) ◽  
pp. 1906-1916 ◽  
Author(s):  
Avijit Chakraborty ◽  
David Okaya
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Seismic Data ◽  
Spectral Decomposition ◽  
Matching Pursuit ◽  
Frequency Resolution ◽  
Short Time Fourier Transform ◽  
Matching Pursuit Algorithm ◽  
Processing Algorithms ◽  
Short Time

Spectral analysis is an important signal processing tool for seismic data. The transformation of a seismogram into the frequency domain is the basis for a significant number of processing algorithms and interpretive methods. However, for seismograms whose frequency content vary with time, a simple 1-D (Fourier) frequency transformation is not sufficient. Improved spectral decomposition in frequency‐time (FT) space is provided by the sliding window (short time) Fourier transform, although this method suffers from the time‐ frequency resolution limitation. Recently developed transforms based on the new mathematical field of wavelet analysis bypass this resolution limitation and offer superior spectral decomposition. The continuous wavelet transform with its scale‐translation plane is conceptually best understood when contrasted to a short time Fourier transform. The discrete wavelet transform and matching pursuit algorithm are alternative wavelet transforms that map a seismogram into FT space. Decomposition into FT space of synthetic and calibrated explosive‐source seismic data suggest that the matching pursuit algorithm provides excellent spectral localization, and reflections, direct and surface waves, and artifact energy are clearly identifiable. Wavelet‐based transformations offer new opportunities for improved processing algorithms and spectral interpretation methods.

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.

scholarly journals Some results for analyzing time-dependent frequencies of vibration signals

2002 ◽  
Vol 24 (1) ◽  
pp. 51-64
Author(s):  
Tran Duong Tri
Keyword(s):  
Spectral Analysis ◽  
Fourier Transform ◽  
Wavelet Transform ◽  
Time Dependent ◽  
Short Time Fourier Transform ◽  
Vibration Signals ◽  
Short Time

This paper provides some results for analyzing relations between frequencies and time of vibration signals. These results have been obtained by studying the properties of wavelet transform, the spectral analysis, the Short-time Fourier transform and by using the toolboxes in the software parked MATLAB. We have created the corresponding PC programs in order to realize algorithms and for the illustration of results by exploring examples.

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