Classification in the Gabor time-frequency domain of non-stationary signals embedded in heavy noise with unknown statistical distribution

Ewa Świercz

International Journal of Applied Mathematics and Computer Science (2010)

  • Volume: 20, Issue: 1, page 135-147
  • ISSN: 1641-876X

Abstract

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A new supervised classification algorithm of a heavily distorted pattern (shape) obtained from noisy observations of nonstationary signals is proposed in the paper. Based on the Gabor transform of 1-D non-stationary signals, 2-D shapes of signals are formulated and the classification formula is developed using the pattern matching idea, which is the simplest case of a pattern recognition task. In the pattern matching problem, where a set of known patterns creates predefined classes, classification relies on assigning the examined pattern to one of the classes. Classical formulation of a Bayes decision rule requires a priori knowledge about statistical features characterising each class, which are rarely known in practice. In the proposed algorithm, the necessity of the statistical approach is avoided, especially since the probability distribution of noise is unknown. In the algorithm, the concept of discriminant functions, represented by Frobenius inner products, is used. The classification rule relies on the choice of the class corresponding to the max discriminant function. Computer simulation results are given to demonstrate the effectiveness of the new classification algorithm. It is shown that the proposed approach is able to correctly classify signals which are embedded in noise with a very low SNR ratio. One of the goals here is to develop a pattern recognition algorithm as the best possible way to automatically make decisions. All simulations have been performed in Matlab. The proposed algorithm can be applied to non-stationary frequency modulated signal classification and non-stationary signal recognition.

How to cite

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Ewa Świercz. "Classification in the Gabor time-frequency domain of non-stationary signals embedded in heavy noise with unknown statistical distribution." International Journal of Applied Mathematics and Computer Science 20.1 (2010): 135-147. <http://eudml.org/doc/207969>.

@article{EwaŚwiercz2010,
abstract = {A new supervised classification algorithm of a heavily distorted pattern (shape) obtained from noisy observations of nonstationary signals is proposed in the paper. Based on the Gabor transform of 1-D non-stationary signals, 2-D shapes of signals are formulated and the classification formula is developed using the pattern matching idea, which is the simplest case of a pattern recognition task. In the pattern matching problem, where a set of known patterns creates predefined classes, classification relies on assigning the examined pattern to one of the classes. Classical formulation of a Bayes decision rule requires a priori knowledge about statistical features characterising each class, which are rarely known in practice. In the proposed algorithm, the necessity of the statistical approach is avoided, especially since the probability distribution of noise is unknown. In the algorithm, the concept of discriminant functions, represented by Frobenius inner products, is used. The classification rule relies on the choice of the class corresponding to the max discriminant function. Computer simulation results are given to demonstrate the effectiveness of the new classification algorithm. It is shown that the proposed approach is able to correctly classify signals which are embedded in noise with a very low SNR ratio. One of the goals here is to develop a pattern recognition algorithm as the best possible way to automatically make decisions. All simulations have been performed in Matlab. The proposed algorithm can be applied to non-stationary frequency modulated signal classification and non-stationary signal recognition.},
author = {Ewa Świercz},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {non-stationary signals; signal classification; pattern recognition; time-frequency transforms},
language = {eng},
number = {1},
pages = {135-147},
title = {Classification in the Gabor time-frequency domain of non-stationary signals embedded in heavy noise with unknown statistical distribution},
url = {http://eudml.org/doc/207969},
volume = {20},
year = {2010},
}

TY - JOUR
AU - Ewa Świercz
TI - Classification in the Gabor time-frequency domain of non-stationary signals embedded in heavy noise with unknown statistical distribution
JO - International Journal of Applied Mathematics and Computer Science
PY - 2010
VL - 20
IS - 1
SP - 135
EP - 147
AB - A new supervised classification algorithm of a heavily distorted pattern (shape) obtained from noisy observations of nonstationary signals is proposed in the paper. Based on the Gabor transform of 1-D non-stationary signals, 2-D shapes of signals are formulated and the classification formula is developed using the pattern matching idea, which is the simplest case of a pattern recognition task. In the pattern matching problem, where a set of known patterns creates predefined classes, classification relies on assigning the examined pattern to one of the classes. Classical formulation of a Bayes decision rule requires a priori knowledge about statistical features characterising each class, which are rarely known in practice. In the proposed algorithm, the necessity of the statistical approach is avoided, especially since the probability distribution of noise is unknown. In the algorithm, the concept of discriminant functions, represented by Frobenius inner products, is used. The classification rule relies on the choice of the class corresponding to the max discriminant function. Computer simulation results are given to demonstrate the effectiveness of the new classification algorithm. It is shown that the proposed approach is able to correctly classify signals which are embedded in noise with a very low SNR ratio. One of the goals here is to develop a pattern recognition algorithm as the best possible way to automatically make decisions. All simulations have been performed in Matlab. The proposed algorithm can be applied to non-stationary frequency modulated signal classification and non-stationary signal recognition.
LA - eng
KW - non-stationary signals; signal classification; pattern recognition; time-frequency transforms
UR - http://eudml.org/doc/207969
ER -

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