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Preface
Chapter 5 considers hidden Markov models (HMMs) for non-
stationary signals. The chapter begins with an introduction to the modelling
of non-stationary signals and then concentrates on the theory and
applications of hidden Markov models. The hidden Markov model is
introduced as a Bayesian model, and methods of training HMMs and using
them for decoding and classification are considered. The chapter also
includes the application of HMMs in noise reduction.
Chapter 6 considers Wiener Filters. The least square error filter is
formulated first through minimisation of the expectation of the squared
error function over the space of the error signal. Then a block-signal
formulation of Wiener filters and a vector space interpretation of Wiener
filters are considered. The frequency response of the Wiener filter is
derived through minimisation of mean square error in the frequency
domain. Some applications of the Wiener filter are considered, and a case
study of the Wiener filter for removal of additive noise provides useful
insight into the operation of the filter.
Chapter 7 considers adaptive filters. The chapter begins with the state-
space equation for Kalman filters. The optimal filter coefficients are
derived using the principle of orthogonality of the innovation signal. The
recursive least squared (RLS) filter, which is an exact sample-adaptive
implementation of the Wiener filter, is derived in this chapter. Then the
steepest−descent search method for the optimal filter is introduced. The
chapter concludes with a study of the LMS adaptive filters.
Chapter 8 considers linear prediction and sub-band linear prediction
models. Forward prediction, backward prediction and lattice predictors are
studied. This chapter introduces a modified predictor for the modelling of
the short−term and the pitch period correlation structures. A maximum a
posteriori (MAP) estimate of a predictor model that includes the prior
probability density function of the predictor is introduced. This chapter
concludes with the application of linear prediction in signal restoration.
Chapter 9 considers frequency analysis and power spectrum estimation.
The chapter begins with an introduction to the Fourier transform, and the
role of the power spectrum in identification of patterns and structures in a
signal process. The chapter considers non−parametric spectral estimation,
model-based spectral estimation, the maximum entropy method, and high−
resolution spectral estimation based on eigenanalysis.
Chapter 10 considers interpolation of a sequence of unknown samples.
This chapter begins with a study of the ideal interpolation of a band-limited
signal, a simple model for the effects of a number of missing samples, and
the factors that affect interpolation. Interpolators are divided into two