scholarly journals Comparative analysis of variants of Gabor-Wigner transform for cross-term reduction

2012 ◽  
Vol 19 (3) ◽  
pp. 499-508 ◽  
Author(s):  
Muhammad Ajab ◽  
Imtiaz Ahmad Taj ◽  
Nabeel Ali Khan
Keyword(s):  
Signal Analysis ◽  
Fractional Fourier Transform ◽  
Wigner Distribution ◽  
Gabor Transform ◽  
Wigner Transform ◽  
Cross Term ◽  
Time Frequency ◽  
Image Processing Techniques ◽  
Cross Terms ◽  
Processing Techniques

Abstract Gabor Wigner Transform (GWT) is a composition of two time-frequency planes (Gabor Transform (GT) and Wigner Distribution (WD)), and hence GWT takes the advantages of both transforms (high resolution of WD and cross-terms free GT). In multi-component signal analysis where GWT fails to extract auto-components, the marriage of signal processing and image processing techniques proved their potential to extract autocomponents. The proposed algorithm maintained the resolution of auto-components. This work also shows that the Fractional Fourier Transform (FRFT) domain is a powerful tool for signal analysis. Performance analysis of modified fractional GWT reveals that it provides a solution of cross-terms of WD and blurring of GT.

A New Form of Gabor Wigner Transform by Adaptive Thresholding in Gabor Transform and Wigner Distribution and the Power of Signal Synthesis Techniques to Enhance the Strengths of GWT

2013 ◽  
Vol 20 (1) ◽  
pp. 99-106
Author(s):  
Muhammad Ajab ◽  
Imtiaz Ahmad Taj ◽  
Imran Shafi ◽  
Srdjan Stankovic
Keyword(s):  
Wigner Distribution ◽  
Adaptive Thresholding ◽  
Gabor Transform ◽  
Combined Effects ◽  
Wigner Transform ◽  
Signal Synthesis ◽  
New Form ◽  
Performance Analyses ◽  
Processing Techniques ◽  
Signal Processing Techniques

Abstract In this paper, a modified form of the Gabor Wigner Transform (GWT) has been proposed. It is based on adaptive thresholding in the Gabor Transform (GT) and Wigner Distribution (WD). The modified GWT combines the advantages of both GT and WD and proves itself as a powerful tool for analyzing multi-component signals. Performance analyses of the proposed distribution are tested on the examples, show high resolution and crossterms suppression. To exploit the strengths of GWT, the signal synthesis technique is used to extract amplitude varying auto-components of a multi-component signal. The proposed technique improves the readability of GWT and proves advantages of combined effects of these signal processing techniques.

Wigner–Ville distribution based on cyclic spectral density and the application in rolling element bearings diagnosis

2011 ◽  
Vol 225 (12) ◽  
pp. 2831-2847 ◽  
Author(s):  
Y Zhou ◽  
J Chen ◽  
G M Dong ◽  
W B Xiao ◽  
Z Y Wang
Keyword(s):  
Fault Diagnosis ◽  
Spectral Density ◽  
Wigner Distribution ◽  
Rolling Element Bearing ◽  
Rolling Element Bearings ◽  
Accurate Analysis ◽  
Time Frequency ◽  
Bearing Fault ◽  
Rolling Element ◽  
Cross Terms

The vibration signals of rolling element bearings are random cyclostationary when they have faults. Also, statistical properties of the signals change periodically with time. The accurate analysis of time-varying signals is an essential pre-requisite for the fault diagnosis and hence safe operation of rolling element bearings. The Wigner distribution is probably most widely used among the Cohen’s class in order to describe how the spectral content of a signal changes over time. However, the basic nature of such signals causes significant interfering cross-terms, which do not permit a straightforward interpretation of the energy distribution. To overcome this difficulty, the Wigner–Ville distribution (WVD) based on the cyclic spectral density (CSD) is discussed in this article. It is shown that the improved WVD, based on CSD of a long time series, can render the time–frequency distribution less susceptible to noise, and restrain the cross-terms in the time–frequency domain. Simulation and experiment of the rolling element-bearing fault diagnosis are performed, and the results indicate the validity of WVD based on CSD in time–frequency analysis for bearing fault detection.

A Direction of Arrival Estimation Method for Wideband LFM Signals Based on RWT and ESPRIT Algorithm

2014 ◽  
Vol 1044-1045 ◽  
pp. 976-981
Author(s):  
Jian Zhong Xu ◽  
Fu Qiang Yu ◽  
Ping Guang Duan ◽  
Shu Hua Li
Keyword(s):  
Frequency Modulation ◽  
Estimation Method ◽  
Direction Of Arrival ◽  
Wigner Transform ◽  
Signal Parameter ◽  
Time Frequency ◽  
Cross Terms ◽  
Stationary Signals ◽  
Simulation Results ◽  
Esprit Algorithm

In this paper, we proposed a new algorithm to estimate the direction of arrival (DOA) for wideband linear frequency modulation (LFM) signals, using Radon-Wigner transform (RWT) and estimation of signal parameter via rotational invariance techniques (ESPRIT). To eliminate the cross-terms, we first utilize the RWT with its excellent time-frequency concentration performance. Then, through peak searching, the number of targets, the initial interference and the frequency modulation slope are estimated. On the this base, the array signals are reconstructed. Finally, we adopt the ESPRIT algorithm to estimate the DOA of the array signals. The simulation results show that the proposed algorithm can estimate the DOA of non-stationary signals with high precision.

scholarly journals A Novel Fractional Filter Design and Cross-Term Elimination in Wigner Distribution

2015 ◽  
Vol 2015 ◽  
pp. 1-12
Author(s):  
Jiexiao Yu ◽  
Kaihua Liu ◽  
Liang Zhang ◽  
Peng Luo
Keyword(s):  
Frequency Distribution ◽  
Filter Design ◽  
Wigner Distribution ◽  
Piecewise Linear ◽  
Support Vector ◽  
Svm Classifier ◽  
Cross Term ◽  
Time Frequency ◽  
Fractional Filter ◽  
Time Frequency Distribution

The second and the third sentences of the abstract are changed and the shorter abstract is given as follows. To recover the nonstationary signal in complicated noise environment without distortion, a novel general design of fractional filter is proposed and applied to eliminate the Wigner cross-term. A time-frequency binary image is obtained from the time-frequency distribution of the observed signal and the optimal separating lines are determined by the support vector machine (SVM) classifier where the image boundary extraction algorithms are used to construct the training set of SVM. After that, the parameters and transfer function of filter can be determined by the parameters of the separating lines directly in the case of linear separability or line segments after the piecewise linear fitting of the separating curves in the case of nonlinear separability. Without any prior knowledge of signal and noise, this method can meet the reliability and universality simultaneously for filter design and realize the global optimization of filter parameters by machine learning even in the case of strong coupling between signal and noise. Furthermore, it could completely eliminate the cross-term in Wigner-Ville distribution (WVD) and the time-frequency distribution we get in the end has high resolution and good readability even when autoterms and cross-terms overlap. Simulation results verified the efficiency of this method.

A New Kind of FRFT Analysis Method for Multi-Component LFM Signals

2011 ◽  
Vol 204-210 ◽  
pp. 973-978
Author(s):  
Qiang Guo ◽  
Ya Jun Li ◽  
Chang Hong Wang
Keyword(s):  
Feature Extraction ◽  
Frequency Analysis ◽  
Signal Analysis ◽  
Fractional Fourier Transform ◽  
Analysis Method ◽  
Time Frequency Analysis ◽  
Time Frequency ◽  
Low Snr ◽  
The Time Domain ◽  
Signal Analysis Method

To effectively detect and recognize multi-component Linear Frequency-Modulated (LFM) emitter signals, a multi-component LFM emitter signal analysis method based on the complex Independent Component Analysis(ICA) which was combined with the Fractional Fourier Transform(FRFT) was proposed. The idea which was adopted to this method was the time-domain separation and then time-frequency analysis, and in the low SNR cases, the problem which is generally plagued by noised of feature extraction of multi-component LFM signal based on FRFT is overcame. Compared to the traditional method of time-frequency analysis, the computer simulation results show that the proposed method for the multi-component LFM signal separation and feature extraction was better.

scholarly journals High Order Chirp Rate Shift Keying Modulation Using the Fractional Fourier Transform

2017 ◽  
Vol 2 (4) ◽  
pp. 1 ◽  
Author(s):  
Seema Sud
Keyword(s):  
Fourier Transform ◽  
Fractional Fourier Transform ◽  
Wigner Distribution ◽  
High Order ◽  
Modulation Scheme ◽  
Chirp Rate ◽  
Bandwidth Utilization ◽  
Time Frequency ◽  
Rate Shift ◽  
Shift Keying

In this paper, we discuss an improved demodulation scheme using the Fractional Fourier Transform (FrFT) for a modulation scheme employing chirp rate shift keying (CrSK). CrSK in conjunction with the FrFT enable very high order, e.g. more than 32-ary modulation schemes to be achievable with good bit error rate (BER) performance, even in the absence of coding, thereby overcoming limitations of traditional schemes including phase shift keying (PSK) or QAM (quadrature amplitude modulation). By using an FrFT-based demodulator, we expand our demodulation degrees of freedom from a single (e.g. frequency) axis to an entire time-frequency domain, called the Wigner Distribution (WD). We show how the proposed demodulation scheme using the FrFT improves over past approaches by more than 7 dB, enabling us to achieve close to 4-ary performance with a 32-ary modulation scheme. This enables future systems to operate at 5 bits/s/Hz bandwidth efficiency, enhancing bandwidth utilization for future generation, high data rate, applications, such as internet.

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