Non-stationary adaptive signal prediction with error bounds
Author(s)
Korale, Asoka J.M.
Type
Thesis
Abstract
A fundamental assumption in autoregressive (AR) modelling is wide sense stationary of the signal. However in practice this assumption may not be satisfied, as the statistics of the signal may be inherently non-stationary. As a consequence, the true AR parameters would be time varying. Therefore if an adaptive predictor which minimises the mean square prediction error was used to estimate the AR parameters the resulting estimates would be inaccurate.
In this work, we depart from the typical assumption of stationarity and examine time varying AR parameter estimation. To account for time dependence a framework based upon a single sample prediction is employed with constraints on the error of prediction. These constraints are introduced in order to bound the prediction error and are used to produce sequential and block-based adaptive predictors. In this context we analyse the effect of using fixed-point iterative procedures on the update equations of the adaptive algorithms. The non-stationary nature of the AR parameters is manifest and taken care of at the next stage.
The AR parameters so obtained are time varying, making efficient signal representation for coding or compression applications difficult. Thus, a new method for the analysis of a non-stationary process is introduced in the context of the “Endomorphic” model. In this model piecewise constant parameters are obtained, when the parameters themselves of an AR process are subject to a multistage AR analysis. This approach is an analysis by synthesis technique where the prediction is formulated as a constrained optimisation problem, which matches the prediction error term to a desired sequence at every sample. We then apply the updates derived for single and multiple constraints on the prediction error, and study the behaviour of the multistage parameters.
We finally consider the case of an HR predictor with a bounded prediction error. In this case, however, the sequential prediction is based on a regression vector of the predicted signal itself. This closed loop prediction, when applied to speech, enables synthesis using a well-defined prediction error signal. The scheme analyses the speech signal into an excitation and a set of AR parameters conditioned on certain a-priori bounds on the prediction error. In this approach, the excitation signal may be used for the determination of the pitch period and glottal closure instants.
In this work, we depart from the typical assumption of stationarity and examine time varying AR parameter estimation. To account for time dependence a framework based upon a single sample prediction is employed with constraints on the error of prediction. These constraints are introduced in order to bound the prediction error and are used to produce sequential and block-based adaptive predictors. In this context we analyse the effect of using fixed-point iterative procedures on the update equations of the adaptive algorithms. The non-stationary nature of the AR parameters is manifest and taken care of at the next stage.
The AR parameters so obtained are time varying, making efficient signal representation for coding or compression applications difficult. Thus, a new method for the analysis of a non-stationary process is introduced in the context of the “Endomorphic” model. In this model piecewise constant parameters are obtained, when the parameters themselves of an AR process are subject to a multistage AR analysis. This approach is an analysis by synthesis technique where the prediction is formulated as a constrained optimisation problem, which matches the prediction error term to a desired sequence at every sample. We then apply the updates derived for single and multiple constraints on the prediction error, and study the behaviour of the multistage parameters.
We finally consider the case of an HR predictor with a bounded prediction error. In this case, however, the sequential prediction is based on a regression vector of the predicted signal itself. This closed loop prediction, when applied to speech, enables synthesis using a well-defined prediction error signal. The scheme analyses the speech signal into an excitation and a set of AR parameters conditioned on certain a-priori bounds on the prediction error. In this approach, the excitation signal may be used for the determination of the pitch period and glottal closure instants.
Date Issued
2000
Date Awarded
2000
Copyright Statement
Creative Commons Attribution NonCommercial NoDerivatives Licence
Advisor
Constantinides, Professor A. G.
Publisher Department
Signal Processing and Digital Systems Section; Electrical and Electronic Engineering.
Publisher Institution
University of London - Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)