A comparison of the existence of 'cross terms' in the Wigner distribution and the squared magnitude of the wavelet transform and the short-time Fourier transform

1992 ◽  
Vol 40 (10) ◽  
pp. 2498-2517 ◽  
Author(s):  
S. Kadambe ◽  
G.F. Boudreaux-Bartels
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Wigner Distribution ◽  
Short Time Fourier Transform ◽  
Cross Terms ◽  
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 Inverting spectrogram measurements via aliased Wigner distribution deconvolution and angular synchronization

2020 ◽  
Author(s):  
Michael Perlmutter ◽  
Sami Merhi ◽  
Aditya Viswanathan ◽  
Mark Iwen
Keyword(s):  
Fourier Transform ◽  
Phase Retrieval ◽  
Wigner Distribution ◽  
Short Time Fourier Transform ◽  
Fourier Inversion ◽  
New Class ◽  
Bandlimited Signals ◽  
Rank One ◽  
Noise Robust ◽  
Short Time

Abstract We propose a two-step approach for reconstructing a signal $\textbf x\in \mathbb{C}^d$ from subsampled discrete short-time Fourier transform magnitude (spectogram) measurements: first, we use an aliased Wigner distribution deconvolution approach to solve for a portion of the rank-one matrix $\widehat{\textbf{x}}\widehat{\textbf{x}}^{*}.$ Secondly, we use angular synchronization to solve for $\widehat{\textbf{x}}$ (and then for $\textbf{x}$ by Fourier inversion). Using this method, we produce two new efficient phase retrieval algorithms that perform well numerically in comparison to standard approaches and also prove two theorems; one which guarantees the recovery of discrete, bandlimited signals $\textbf{x}\in \mathbb{C}^{d}$ from fewer than $d$ short-time Fourier transform magnitude measurements and another which establishes a new class of deterministic coded diffraction pattern measurements which are guaranteed to allow efficient and noise robust recovery.

scholarly journals Zeros of the Wigner distribution and the short-time Fourier transform

2019 ◽  
Vol 33 (3) ◽  
pp. 723-744 ◽  
Author(s):  
Karlheinz Gröchenig ◽  
Philippe Jaming ◽  
Eugenia Malinnikova
Keyword(s):  
Fourier Transform ◽  
Bessel Functions ◽  
Wigner Distribution ◽  
Short Time Fourier Transform ◽  
Step Functions ◽  
Wigner Distributions ◽  
Hurwitz Polynomials ◽  
Totally Positive ◽  
Short Time ◽  
Positive Functions

AbstractWe study the question under which conditions the zero set of a (cross-) Wigner distribution W(f, g) or a short-time Fourier transform is empty. This is the case when both f and g are generalized Gaussians, but we will construct less obvious examples consisting of exponential functions and their convolutions. The results require elements from the theory of totally positive functions, Bessel functions, and Hurwitz polynomials. The question of zero-free Wigner distributions is also related to Hudson’s theorem for the positivity of the Wigner distribution and to Hardy’s uncertainty principle. We then construct a class of step functions S so that the Wigner distribution $$W(f,\mathbf {1}_{(0,1)})$$ W ( f , 1 ( 0 , 1 ) ) always possesses a zero $$f\in S \cap L^p$$ f ∈ S ∩ L p when $$p<\infty $$ p < ∞ , but may be zero-free for $$f\in S \cap L^\infty $$ f ∈ S ∩ L ∞ . The examples show that the question of zeros of the Wigner distribution may be quite subtle and relate to several branches of analysis.

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.

Using ASTFT Spectrum to Suppress Cross Terms in WVD and its Application in Fault Diagnosis

2009 ◽  
Vol 626-627 ◽  
pp. 535-540
Author(s):  
B.P. Tang ◽  
F. Li ◽  
W.Y. Liu
Keyword(s):  
Feature Extraction ◽  
Fourier Transform ◽  
Fault Diagnosis ◽  
Short Time Fourier Transform ◽  
Time Frequency ◽  
Effective Suppression ◽  
Cross Terms ◽  
Diagnosis Method ◽  
Simulation Results ◽  
Short Time

A new fault diagnosis method to suppress cross terms of Wigner-Ville distribution (WVD) using Adaptive Short-time Fourier Transform (ASTFT) spectrum is put forward. The relationships of correlation between auto terms and cross terms of WVD are obtained theoretically by analyzing the WVD. Firstly, the signal ASTFT spectrum which can determine the signal component positions in the time-frequency plane is obtained. Then, the ASTFT spectrum as a window function is selected to process the signal WVD. Thus the cross terms can be effectively restrained. The simulation results show that a better resolution and more effective suppression of cross terms can be obtained. At last, the proposed method is applied to the fault diagnosis of bearing. The simulation and the experiment results indicate that the proposed method is effective in feature extraction.

Sign in / Sign up

Export Citation Format

Share Document