Linear prediction

Linear prediction is a mathematical operation where future values of a discrete-time signal are estimated as a linear function of previous samples. In digital signal processing, linear prediction is often called linear predictive coding (LPC) and can thus be viewed as a subset of filter theory. In system analysis, a subfield of mathematics, linear prediction can be viewed as a part of mathematical modelling or optimization. The prediction model The most common representation is :\widehat{x}(n) = \sum_{i=1}^p a_i x(n-i), where \widehat{x}(n) is the predicted signal value, x(n-i) the previous observed values, with p \leq n , and a_i the predictor coefficients. The error generated by this estimate is :e(n) = x(n) - \widehat{x}(n), where x(n) is the true signal value. These equations are valid for all types of (one-dimensional) linear prediction. The differences are found in the

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications (8)

Related publications

Related people

Related units

Related concepts (6)

Related concepts

Related courses (11)

Related courses

Related lectures (18)

Related lectures

Using Polynomials to Forecast Univariate Time Series

Polynomial autoregressions have been most of the time discarded as being unrealistic. Indeed, for such processes to be stationary, strong assumptions on the parameters and on the noise are necessary. For example, the distribution of the latter has to have finite support. Nevertheless, the use of polynomials has been advocated by a few authors: Cox (1991), Cobb and Zacks (1988) and Chan and Tong (1994). From a model-free perspective, that is using parametric families of functions (e.g. Fourier series, wavelets, neural networks, MARS, ...) as approximators of the optimal predictor, there is no more concern about stationarity. Still, polynomials have not been used within this framework; the reason is the now well known "curse of dimensionality". Indeed, when high lag orders are used to forecast, a common situation in time series, polynomial autoregressions imply too many parameters to estimate. We will introduce a new family of predictors based on polynomials and on a projection scheme. A censoring procedure allows to solve the instability inherent to polynomials. The forecasting method is parsimonious (that is non-linearity is introduced with a small amount of parameters) and thus allows to forecast noisy time series of short to moderate length.

1996

Joint Source-Filter Optimization for Accurate Vocal Tract Estimation Using Differential Evolution

Olaf Schleusing, Jean-Marc Vesin

In this work, we present a joint source-filter optimization approach for separating voiced speech into vocal tract (VT) and voice source components. The presented method is pitch-synchronous and thereby exhibits a high robustness against vocal jitter, shimmer and other glottal variations while covering various voice qualities. The voice source is modeled using the Liljencrants-Fant (LF) model, which is integrated into a time-varying auto-regressive speech production model with exogenous input (ARX). The non-convex optimization problem of finding the optimal model parameters is addressed by a heuristic, evolutionary optimization method called differential evolution. The optimization method is first validated in a series of experiments with synthetic speech. Estimated glottal source and VT parameters are the criteria used for comparison with the iterative adaptive inverse filter (IAIF) method and the linear prediction (LP) method under varying conditions such as jitter, fundamental frequency (f(0)) as well as environmental and glottal noise. The results show that the proposed method largely reduces the bias and standard deviation of estimated VT coefficients and glottal source parameters. Furthermore, the performance of the source-filter separation is evaluated in experiments using speech generated with a physical model of speech production. The proposed method reliably estimates glottal flow waveforms and lower formant frequencies. Results obtained for higher formant frequencies indicate that research on more accurate voice source models and their interaction with the VT is necessary to improve the source-filter separation. The proposed optimization approach promises to be a useful tool for future research addressing this topic.

Ieee-Inst Electrical Electronics Engineers Inc2013

Linear Autoregression for Prediction: Small Sample Inference

This paper describes inferences based on linear predictors for stationary time series. These methods are flexible, since relatively few assumptions are needed to fit a linear predictor. A confidence interval for the resulting predicted value, which takes account of the variance of the estimated parameters, is discussed. The possible non-parsimony of the linear prediction compared to the classical ARMA forecasting method is a drawback often mentioned in the literature. On the other hand, as we show in a small simulation study, the usual predictive inference based on an ARMA modelling is overoptimistic in small samples, whereas the coverage rate of our confidence interval is close to the nominal value even for small series.

1993

Linear predictive coding

Linear predictive coding (LPC) is a method used mostly in audio signal processing and speech processing for representing the spectral envelope of a digital signal of speech in compressed form, using t

Adaptive filter

An adaptive filter is a system with a linear filter that has a transfer function controlled by variable parameters and a means to adjust those parameters according to an optimization algorithm. Beca

Wiener filter

In signal processing, the Wiener filter is a filter used to produce an estimate of a desired or target random process by linear time-invariant (LTI) filtering of an observed noisy process, assuming

EE-512: Applied biomedical signal processing

The goal of this course is twofold: (1) to introduce physiological basis, signal acquisition solutions (sensors) and state-of-the-art signal processing techniques, and (2) to propose concrete examples of applications for vital sign monitoring and diagnosis purposes.

COM-500: Statistical signal and data processing through applications

Building up on the basic concepts of sampling, filtering and Fourier transforms, we address stochastic modeling, spectral analysis, estimation and prediction, classification, and adaptive filtering, with an application oriented approach and hands-on numerical exercises.

EE-350: Signal processing

Dans ce cours, nous présentons les méthodes de base du traitement des signaux.