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Kalman filter is normally used to enhance speech quality in a noisy environment, in which the speech signals are usually modelled as autoregressive (AR) process, and represented in the state-space domain. It is a known fact that to identify the changing AR coefficients in every time state requires extensive computation. In this paper, the authors develop a bidirectional Kalman filter and apply it in a speech processing system. The proposed filter uses a system dynamics model that utilises the past and the future measurements to form an estimate of the system's current time state. It provides efficient recursive means to estimate the state of a process that minimises the mean of the squared error. Compared to the conventional Kalman filter, the proposed filter reduces the computation time in two ways: (i) by avoiding the computation of AR parameters in each time state, and (ii) by reducing the dimension of the matrices involved in the difference equations and the measurement equations into constant (1 × 1) matrices. The speech recognition result shows that the developed speech recognition system becomes more robust after the proposed filtering process, and the proposed filter's low computational expense makes it applicable in the practical hidden Markov model-based speech recognition system.

In this study, the authors propose a speech recognition system using harmonic structure related information to detect harmonic features in noisy environment. The proposed algorithm first extracts the harmonic components contained inside the speech signals using sine function convolution. By setting the frequency of the sine function as equal to the fundamental frequency of speech signals, harmonic components can be extracted out. The reconstructed signal obtained by summing up the extracted harmonic components is found to have a high degree of correlation with the original signal. The extracted frame energy measure of the harmonic components has been further processed to become dynamic harmonic features and then used together with the European Telecommunications Standards Institute (ETSI) front-end processed mel-frequency cepstral coefficients (MFCC) feature or the perceptual linear prediction (PLP) feature in the speech recognition system. The proposed enhanced speech recognition system shows a better recognition rate over the ETSI front-end processed MFCC (or PLP)-based speech recognition system.

This study introduces a new set of orthogonal polynomials and moments and the set's application in signal and image processing. This polynomial is derived from two well-known orthogonal polynomials: the Tchebichef and Krawtchouk polynomials. This study attempts to present the following: (i) the mathematical and theoretical frameworks for the definition of this polynomial including the modelling of signals with the various analytical properties it contains, as well as, recurrence relations and transform equations that need to be addressed; and (ii) the results of empirical tests that compare the representational capabilities of this polynomial with those of the more traditional Tchebichef and Krawtchouk polynomials using speech and image signals from different databases. This study attempts to demonstrate that the proposed polynomials can be applied in the field of signal and image processing because of the promising properties of this polynomial especially in its localisation and energy compaction capabilities.