NON STATIONARY SIGNALS ANALYSIS BY TEAGER-HUANG TRANSFORM(THT)

By A.Roja

KL University

arojaroja12@gmail.com

Overview

• Objective• Introduction• Existing Methods• Drawbacks• Proposed Method• Status of the Project• Expected Results• Conclusion• References

Objective

• The Objective of the project is to analyze the non-stationary signals by using Teager-Huang Transform by estimating the Instantaneous Frequency (IF) and Instantaneous Amplitude (IA) .

Introduction

• In many areas such as in seismic, radar, sonar, telecommunications, biomedicine signals under consideration are known to be Non-Stationary.• An important feature of non-stationary signals is provided by its IF, which accounts for the spectral variations as a function of time and also IF is used to define the local characteristics of a non stationary signal.

Existing Methods

• Fast Fourier Transform • Time Frequency Analysis Methods• Short Time Fourier Transform• Wavelet Transform• Wigner Ville Distribution• Pseudo Wigner Ville Distribution

• Hilbert Huang Transform

Fast Fourier Transform

• The Fast Fourier Transform can be used to analyse the frequency features of stationary signals.

• The FFT spectrum are not suitable for non stationary signal analysis and are also unable to show components with low energy clearly.

• The major drawback of FFT is lost in time information when transforming into frequency domain.

Time Frequency Analysis Methods

• Time Frequency analysis is an effective tool for analysing the signal whose spectral components change with time.

• The basic idea of time frequency analysis is to design a joint function which can describe the characteristics of the signals on the time frequency plane.

Figure of TF Plane

Short Time Fourier Transform

• In STFT, a non stationary signal is split into fractions by a window function, which can be regarded as stationary signals.

• These fractions are treated by Fourier Transform to find its frequency components.

• The major drawback of STFT is that once the particular size time window is chosen, the window remains same for all frequencies.

Wavelet Transform

• The wavelet Transform was developed to overcome the shortcomings of STFT.

• The WT uses a multi resolution technique by which different frequencies are analysed with different resolution.

• The major drawback is that the wavelet must be rescaled in order to extract the frequency content of the signal at frequencies other than the frequency of the basic wavelet.

Wigner Ville Distribution

• The WVD is an analysis technique that also provide an energy distribution of the signal in both time and frequency domain.

• The main characteristics of this transform is that it does not place any restriction on the simultaneous resolution in time and in frequency.

• The drawback of this method is that it leads to the emergence of negative energy levels and cross terms and there is also problem with signal multiplication.

Pseudo Wigner Ville Distribution

• The gain in resolution is compensated by the loss of clarity of the time frequency energy distribution diagram in WVD.• The time resolution for the PWVD is the sampling interval, while the frequency resolution obtained is directly related to the length of the chosen window.• The drawback is that there is loss in frequency resolution and cross terms are superposed on the signal components.

Hilbert Huang Transform

• Empirical Mode Decomposition (EMD) is the process of decomposing the signal into Implicit Mode Functions (IMFs).

• The Hilbert Transform is applied to each IMFs, yielding a time-frequency representation.

• The major drawbacks of HHT are End Effect and Mode Mixing.

Proposed Method

•To overcome the shortcomings of above methods, a new method called Teager-Huang Transform(THT) is introduced.•The THT estimates the IF and IA of a signal.•The method is based on Complete Ensemble Empirical Mode Decomposition (CEEMD) and Teager Energy Operator(TEO).

Status of the Project

• The existing methods and it’s drawbacks are studied.• The generation of code for Non Stationary Signals

Analysis is in progress.

Expected Results

Pseudo Wigner Ville Distribution

Hilbert Huang Transform

Teager Huang Transform

Conclusion

• The THT can be easily implemented and Energy-frequency-time distribution can be designed for processing any data (linear or non-linear) and stationary or non-stationary signals with free of interference.

References

• Jean-Christophe Cexus and Abdel-Ouahab Boudraa, “Non stationary Signals Analysis by Teager-huang Transform (THT),” 14th European Signal Processing Conference (EUSIPCO 2006), Florence, Italy, September 4-8, 2006.

• N.E. Huang et al., ”The empirical mode decomposition and the Hilbert spectrum for nonlinear and non stationary time series analysis,” Proc. Royal Soc. London A, vol. 454, pp. 903-995, 1998.

• P. Flandrin, G. Rilling, and P. Goncalves, “Empirical mode decomposition as a filter bank,” IEEE Sig. Proc. Lett., vol.11, no. 2, pp. 112–114, 2004.

• S. Mallat, “A Theory for Multi-Resolution Signal Decomposition Wavelet Representation,” IEEE Trans. On Pattern Analysis and Machine Intell. 11(7), 674-693, 1989.