Pole-Zero modeling and its applications to speech processing

technical reportAutocorrelation Pole-Zero modeling identifies the parameters of a rational transfer function H(z) whose short time-lag autocorrelations either exactly match (Autocorrelation partial Realization) or closely approximate (Autocorrelation Prediction) those of a given spectrum. As a result, the spectrum of the H(z) obtained from either method approximates the gross structure of the given spectrum. Autocorrelation Partial Realization (APR) uses the Pade approximation to determine the denominator coefficients of H(z). To compute the numerator coefficients of H(z), APR uses an iterative algorithm such as Fejer's or Newton-Raphson's. In contrast, Autocorrelation Prediction (AP) uses only Linear Prediction (LP) to determine both the denominator and numerator coefficients. Therefore, once the autocorrelation function of the given spectrum is known, AP uses only linear operations and no Fourier Transformations to determine the parameters of H(z). Moreover, the resulting rational transfer function is guaranteed to be minimum phase and consequently stable . AP can also automatically determine the least (parsimonious) denominator and numerator orders required to model efficiently a given spectral envelope. A dynamic filtering process, based on Wiener filtering and Autocorrelation Prediction, was developed to suppress the background noise from degraded speech. More important, using AP, a Linear Predictive Vocoder was integrated into the so called "Pole-Zero Vocoder"(PZV). Computer simulations of both, the dynamic filtering process and the PZV were successfully used in speech processing

Sparsity in Linear Predictive Coding of Speech

nrpages: 197status: publishe

Time-Resolved Method for Spectral Analysis based on Linear Predictive Coding, with Application to EEG Analysis

EEG (Electroencephalogram) signal is a biological signal in BCI (Brain-Computer Interface) systems to realise the information exchange between the brain and the external environment. It is characterised by a poor signal-to-noise ratio, is time-varying, is intermittent and contains multiple frequency components. This research work has developed a new parameterised time-frequency method called the Linear Predictive Coding Pole Processing (LPCPP) method which can be used for identifying and tracking the dominant frequency components of an EEG signal. The LPCPP method further processes LPC (Linear Predictive Coding) poles to produce a series of reduced-order filter transfer functions to estimate the dominant frequencies. It is suited for processing high-noise multi-component signals and can directly give the corresponding frequency estimates unlike transform-based methods. Furthermore, a new EEG spectral analysis framework involving the LPCPP method is proposed to describe the EEG spectral activity. The EEG signal has been divided into different frequency bands (i.e. Delta, Theta, Alpha, Beta and Gamma). However, there is no consensus on the definitions of these band boundaries. A series of EEG centre frequencies are proposed in this thesis instead of fixed frequency boundaries, as they are better suited to describe the dominant EEG spectral activity

A Linear Predictive Coding Filtering Method for Time-resolved Morphology of EEG Activity

This paper introduces a new time-resolved spectral analysis method based on the Linear Prediction Coding (LPC) method that is particularly suited to the study of the dynamics of EEG (Electroencephalography) activity. The spectral dynamics of EEG signals can be challenging to analyse as they contain multiple frequency components and are often corrupted by noise. The LPC Filtering (LPCF) method described here processes the LPC poles to generate a series of reduced-order filter transform functions which can accurately estimate the dominant frequencies. The LPCF method is a parameterized time-frequency method that is suitable for identifying the dominant frequencies of multiple-component signals (e.g. EEG signals). We define bias and the frequency resolution metrics to assess the ability of the LPCF method to estimate the frequencies. The experimental results show that the LPCF can reduce the bias of the LPC estimates in the low and high frequency bands and improved frequency resolution. Furthermore, the LPCF method is less sensitive to the filter order and has a higher tolerance of noise compared to the LPC method. Finally, we apply the LPCF method to a real EEG signal where it can identify the dominant frequency in each frequency band and significantly reduce the redundant estimates of the LPC method

Novel modeling of task versus rest brain state predictability using a dynamic time warping spectrum: comparisons and contrasts with other standard measures of brain dynamics

Dynamic time warping, or DTW, is a powerful and domain-general sequence alignment method for computing a similarity measure. Such dynamic programming-based techniques like DTW are now the backbone and driver of most bioinformatics methods and discoveries. In neuroscience it has had far less use, though this has begun to change. We wanted to explore new ways of applying DTW, not simply as a measure with which to cluster or compare similarity between features but in a conceptually different way. We have used DTW to provide a more interpretable spectral description of the data, compared to standard approaches such as the Fourier and related transforms. The DTW approach and standard discrete Fourier transform (DFT) are assessed against benchmark measures of neural dynamics. These include EEG microstates, EEG avalanches, and the sum squared error (SSE) from a multilayer perceptron (MLP) prediction of the EEG time series, and simultaneously acquired FMRI BOLD signal. We explored the relationships between these variables of interest in an EEG-FMRI dataset acquired during a standard cognitive task, which allowed us to explore how DTW differentially performs in different task settings. We found that despite strong correlations between DTW and DFT-spectra, DTW was a better predictor for almost every measure of brain dynamics. Using these DTW measures, we show that predictability is almost always higher in task than in rest states, which is consistent to other theoretical and empirical findings, providing additional evidence for the utility of the DTW approach

A sample selective linear predictive analysis of speech signals

The Linear Prediction Analysis is one of the popular methods of processing speech. But it has problems in estimating the vocal tract characteristics of voiced sounds uttered by females and children. This is because the conventional linear prediction method assumes that all the sample values in each analysis frame are to be approximated by a linear combination of a definite number of the previous samples whether the previous samples include excitation periods or not. Also, the Linear Prediction analysis is easily affected by source excitation; The vocal tract characteristics of signals of short pitch period can be estimated more accurately by the Sample Selective Linear Prediction (SSLP). The first stage of a SSLP analysis is the conventional linear predictive analysis and in the second stage, only those samples which are under a specified threshold are used for further analysis; This work outlines a numerically stable algorithm for performing the SSLP using the Autocorrelation method. (Abstract shortened by UMI.)