Prakash Kumar Sahu

Legendre wavelets operational method for the numerical solutions of nonlinear Volterra integro-differential equations system

In this paper, Legendre wavelet method is developed to approximate the solutions of system of nonlinear Volterra integro-differential equations. The properties of Legendre wavelets are first presented. The properties of Legendre wavelets are used to reduce the system of integral equations to a system of algebraic equations which can be solved numerically by Newtons method. Also, the results obtained by present method have been compared with that of by B-spline wavelet method. Illustrative examples have been discussed to demonstrate the validity and applicability of the present method.

Admissible wavelet packet features based on human inner ear frequency response for Hindi consonant recognition

Graphical abstractDisplay Omitted 24 Subband WP decomposition according to the auditory ERB scale.Variance feature added to make features more robust.Hindi consonants recognition task has been carried out.Special attention given to Hindi unvoiced phonemes specially stops.Improved performance with proposed feature. It was observed that for non-stationary and quasi-stationary signals, wavelet transform has been found to be an effective tool for the time-frequency analysis. In the recent years wavelet transform being used for feature extraction in speech recognition applications. Here a new filter structure using admissible wavelet packet analysis is proposed for Hindi phoneme recognition. These filters have the benefit of having frequency bands spacing similar to the auditory Equivalent Rectangular Bandwidth (ERB) scale whose central frequencies are equally distributed along the frequency response of human cochlea. The phoneme recognition performance of proposed feature is compared with the standard baseline features and 24-band admissible wavelet packet-based features using a Hidden Markov Model (HMM) based classifier. Proposed feature shows better performance compared to conventional features for Hindi consonant recognition. To evaluate the robustness of proposed feature in the noisy environment NOISEX-92 database has been used.

Two-dimensional Legendre wavelet method for the numerical solutions of fuzzy integro-differential equations

In this paper, two dimensional Legendre wavelet method has been applied to solve the fuzzy integro-differential equations. The properties of Legendre wavelets are first presented. In fuzzy case, we have developed two dimensional Legendre wavelets to approximate the fuzzy integro-differential equations. The properties of Legendre wavelets are used to reduce the system of integral equations to a system of algebraic equations which can be solved by any usual numerical method. Illustrative examples have been discussed to demonstrate the validity and applicability of the present method.

Numerical solutions for the system of Fredholm integral equations of second kind by a new approach involving semiorthogonal B-spline wavelet collocation method

In this paper, a new approach based on linear B-spline wavelet method has been developed to approximate the solutions of system of linear Fredholm integral equations of second kind. Compactly supported linear semi-orthogonal B-spline scaling functions and wavelet functions together with their dual functions are applied to approximate the solutions of linear Fredholm integral equations system of second kind. This method reduces the system of integral equations to a linear system of algebraic equations that can be solved easily with any of the usual methods. The numerical results obtained by the present method have been compared with those obtained by adaptive method based on Trapezoidal rule. Numerical examples are presented to illustrate the accuracy of the method.

Feature extraction technique using ERB like wavelet sub-band periodic and aperiodic decomposition for TIMIT phoneme recognition

In the recent years, wavelet transform has been found to be an effective tool for the time–frequency analysis for non-stationary and quasi-stationary signals such as speech signals. In the recent past, wavelet transform has been used as feature extraction in speech recognition applications. Here we propose a wavelet based feature extraction technique that signifies both the periodic and aperiodic information along with sub-band instantaneous frequency of speech signal for robust speech recognition in noisy environment. This technique is based on parallel distributed processing technique inspired by the human speech perception process. This frontend feature processing technique employs equivalent rectangular bandwidth (ERB) filter like wavelet speech feature extraction method called Wavelet ERB Sub-band based Periodicity and Aperiodicity Decomposition (WERB-SPADE), and examines its validity for TIMIT phone recognition task in noisy environments. The speech sound is filtered by 24 band ERB like wavelet filter banks, and then the equal loudness pre-emphasized output of each band is processed through comb filter. Each comb filter is designed individually for each frequency sub-band to decompose the signal into periodic and aperiodic features. Thus it takes the advantage of the robustness shown by periodic features without losing certain important information like formant transition incorporated in aperiodic features. Speech recognition experiments with a standard HMM recognizer under both clean-training and multi-training condition training is conducted. Proposed technique shows more robustness compared to other features especially in noisy condition.

Numerical Methods for Solving Fredholm Integral Equations of Second Kind

Integral equation has been one of the essential tools for various areas of applied mathematics. In this paper, we review different numerical methods for solving both linear and nonlinear Fredholm integral equations of second kind. The goal is to categorize the selected methods and assess their accuracy and efficiency. We discuss challenges faced by researchers in this field, and we emphasize the importance of interdisciplinary effort for advancing the study on numerical methods for solving integral equations.

Legendre spectral collocation method for Fredholm integro-differential-difference equation with variable coefficients and mixed conditions

In this article, the Legendre spectral collocation method has been applied to solve Fredholm integro-differential-difference equations with variable coefficients. The proposed method is based on the Gauss-Legendre points with the basis functions of Lagrange polynomials. Usually, this type of integral equations are very difficult to solve analytically as well as numerically. The presented method applied to the integral equation reduces to solve the system of algebraic equations. Also the numerical results obtained by Legendre spectral collocation method have been compared with the results obtained by existing methods. Illustrative examples have been discussed to demonstrate the validity and applicability of the presented method.

Hindi phoneme classification using Wiener filtered wavelet packet decomposed periodic and aperiodic acoustic feature

Display Omitted 24 subband WP decomposition according to the auditory ERB scale.Proposed wavelet subband specific periodic and aperiodic decomposition.Wiener filter is used at frontend for noise minimization.Hindi phoneme classification task has been carried out.Proposed technique outperforms others classify voiced phonemes. Wavelet packet (WP) acoustic features are found to be very promising in unvoiced phoneme classification task but they are less effective to capture periodic information from voiced speech. This motivated us to develop a wavelet packet based feature extraction technique that signifies both the periodic and aperiodic information. This method is based on parallel distributed processing technique inspired by the human speech perception process. This front end feature processing technique employs Equivalent Rectangular Bandwidth (ERB) filter like wavelet speech feature extraction method called Wavelet ERB Sub-band based Periodicity and Aperiodicity Decomposition (WERB-SPADE). Winer filter is used at front end to minimize the noise for further processing. The speech signal is filtered by 24 band ERB like wavelet filter banks, and then the output of each sub-band is processed through comb filter. Each comb filter is designed individually for each sub-band to decompose the signal into periodic and aperiodic features. Thus it carries the periodic information without losing certain important information like formant transition incorporated in aperiodic features. Hindi phoneme classification experiments with a standard HMM recognizer under both clean-training and multi-training condition is conducted. This technique shows significant improvement in voiced phoneme class without affecting the performance of unvoiced phoneme class.

A new Bernoulli wavelet method for accurate solutions of nonlinear fuzzy Hammerstein-Volterra delay integral equations

In this article, Bernoulli wavelet method has been developed to solve nonlinear fuzzy Hammerstein-Volterra integral equations with constant delay. This type of integral equation has a particular case the fuzzy variant of a mathematical model from epidemiology. Bernoulli wavelets have been generated by dilation and translation of Bernoulli polynomials. The properties of Bernoulli wavelets and Bernoulli polynomials are first presented. The present wavelet method reduces these integral equations to a system of nonlinear algebraic equations and again these algebraic systems have been solved numerically by Newtons method. Convergence analysis of the present method has been discussed in this article. Also the results obtained by present wavelet method have been compared with that of by B-spline wavelet method. Some illustrative examples have been demonstrated to show the applicability and accuracy of the present method.

Multiple cameras audio visual speech recognition using active appearance model visual features in car environment

Consideration of visual speech features along with traditional acoustic features have shown decent performance in uncontrolled auditory environment. However, most of the existing audio-visual speech recognition (AVSR) systems have been developed in the laboratory conditions and rarely addressed the visual domain problems. This paper presents an active appearance model (AAM) based multiple-camera AVSR experiment. The shape and appearance information are extracted from jaw and lip region to enhance the performance in vehicle environments. At first, a series of visual speech recognition (VSR) experiments are carried out to study the impact of each camera on multi-stream VSR. Four cameras in car audio-visual corpus is used to perform the experiments. The individual camera stream is fused to have four-stream synchronous hidden Markov model visual speech recognizer. Finally, optimum four-stream VSR is combined with single stream acoustic HMM to build five-stream AVSR. The dual modality AVSR system shows more robustness compared to acoustic speech recognizer across all driving conditions.