Christian Gargour

A short introduction to wavelets and their applications

This simplified introduction to wavelets starts with a short historical background. The continuous wavelet transform is presented. The multiresolution concept is concisely described. It is followed by the filter banks method for wavelet analysis and reconstruction. Wavelet packets are briefly presented. Some typical applications are mentioned.

Implementation of a stability test of 1-D discrete system based on Schussler's theorem and some consequent coefficient conditions

Abstract Based on Schusslers theorem, some new properties of polynomials containing zeros inside the unit circle are obtained. These properties give rise to (i) a new stability test of 1-D discrete systems, and (ii) some necessary coefficient conditions that have to be satisfied by the denominator polynomial of a stable 1-D discrete system.

Wavelet based speech enhancement using two different threshold-based denoising algorithms

In this paper, we present a wavelet-based speech denoising technique obtained by the combination of the /spl mu/-law thresholding and the soft thresholding algorithm. Denoising is a compromise between the removal of the largest possible amount of noise and the preservation of signal integrity. To achieve a good implementation of this compromise we purpose the following procedure. The signal to be denoised is decomposed using wavelet packets up to the seventh level using DB11 wavelets. The /spl mu/-law thresholding is applied to all the final decomposition level subband coefficients except those of the two lower subbands on which soft thresholding is applied. To evaluate the performance of the proposed method, a clean speech dataset from the TIMIT database, corrupted with pink noise, for SNR levels ranging from 5 to 15 dB has been utilized. It has been found that the results obtained by our method are better than those given by each one of the two combined methods used separately.

Automated pathologies detection in retina digital images based on complex continuous wavelet transform phase angles

An automated diagnosis system that uses complex continuous wavelet transform (CWT) to process retina digital images and support vector machines (SVMs) for classification purposes is presented. In particular, each retina image is transformed into two one-dimensional signals by concatenating image rows and columns separately. The mathematical norm of phase angles found in each one-dimensional signal at each level of CWT decomposition are relied on to characterise the texture of normal images against abnormal images affected by exudates, drusen and microaneurysms. The leave-one-out cross-validation method was adopted to conduct experiments and the results from the SVM show that the proposed approach gives better results than those obtained by other methods based on the correct classification rate, sensitivity and specificity.

Design of 2-D recursive digital filters with constant group delay characteristics using separable denominator transfer function and a new stability test

In this paper, based on a new stability test, two 1-D polynomials in z 1 and z 2 having all their zeros inside the unit circles in z 1 and z 2 planes are generated and assigned to the denominator of a separable denominator 2-D transfer function while the numerator is left to a 2-D nonseparable polynomial in z 1 and z 2 . Now any suitable nonlinear optimization technique can be used to calculate the parameters of the 2-D filter in such a way so as to minimize the general mean square error between the ideal and the designed magnitude and group delay responses of the 2-D filter subject to the coefficient constraints given by the new stability test. To illustrate the method, an example is given.

Direct design of recursive digital filters based on a new stability test

Abstract In this paper we present an alternative approach to the direct design of 1-D recursive digital filters satisfying prescribed magnitude specifications with or without constant group delay characteristic. This method uses an iterative method to calculate the coefficients of the filters transfer function and guarantees the stability of the designed filter using a new stability test reported by Ramachandran and Gargour. To illustrate the usefulness of the technique, examples are given.

Variable magnitude characteristics of 1-D IIR discrete filters by a generalized bilinear transformation

It is shown that variable magnitude characteristics can be obtained by the application of a general bilinear transformation of the type s/spl rarr/(a/sub 1/z+a/sub 0/)/(b/sub 1/z+b/sub 0/) to a known analog filter. Stability considerations dictate the limits of the values of a/sub 1/, a/sub 0/, b/sub 1/ and b/sub 0/; and these limits have been determined. Starting from some known filter characteristics in the analog domain, it is shown that different magnitude characteristics can be obtained in the discrete domain.

Generation of digital transfer functions of the FIR type approximating z/sup -p/q/

It is shown that a polynomial approximation of z/sup -p/q/ is possible. The method of obtaining the various coefficients of the polynomial is given. The case of z/sup -1/2/ is discussed in detail. It is shown that it is possible to optimize the coefficients of the polynomial so as to minimize the sum of the squares of the error between the response and the ideal one. The responses considered can be magnitude, phase, or group delay, and as a consequence, a combination of magnitude and group delay responses.<<ETX>>

Variable magnitude 2-D lowpass filters having nonseparable denominators generated from separable functions

Two-dimensional transfer functions for obtaining variable magnitude characteristics are generated starting from product separable denominators. Conditions for stability are obtained. Examples illustrate how a single parameter can be varied to obtain variable magnitude characteristics.<<ETX>>

A scheme for teaching wavelets at the introductory level

Wavelet analysis and synthesis are becoming highly important in the area of signal processing. Therefore, it is felt that undergraduate electrical engineering students should be exposed to the rudiments of this treatment before they graduate. A scheme for an elementary coverage of this topic with required minimum amount of mathematics is discussed in this paper.