Abstract
While linear prediction (LP) has become immensely popular in speech modeling, it does not seem to provide a good approach for modeling audio signals. This is somewhat surprising, since a tonal signal consisting of a number of sinusoids can be perfectly predicted based on an (all-pole) LP model with a model order that is twice the number of sinusoids. We provide an explanation why this result cannot simply be extrapolated to LP of audio signals. If noise is taken into account in the tonal signal model, a low-order all-pole model appears to be only appropriate when the tonal components are uniformly distributed in the Nyquist interval. Based on this observation, different alternatives to the conventional LP model can be suggested. Either the model should be changed to a pole-zero, a high-order all-pole, or a pitch prediction model, or the conventional LP model should be preceded by an appropriate frequency transform, such as a frequency warping or downsampling. By comparing these alternative LP models to the conventional LP model in terms of frequency estimation accuracy, residual spectral flatness, and perceptual frequency resolution, we obtain several new and promising approaches to LP-based audio modeling.
Highlights
Linear prediction (LP) is a widely used and well-understood technique for the analysis, modeling, and coding of speech signals [1]
In the last two alternative LP models, namely, the warped LP (WLP) model and the selective LP (SLP) model, the performance of the conventional low-order all-pole model is increased by first transforming the input signal such that its tonal components are spread in the entire Nyquist interval
We evaluate the conventional and alternative LP models described in Sections 3 and 4 in terms of frequency estimation accuracy, residual spectral flatness, and perceptual frequency resolution for a synthetic harmonic audio signal with varying fundamental frequency and signal-to-noise ratio (SNR)
Summary
Linear prediction (LP) is a widely used and well-understood technique for the analysis, modeling, and coding of speech signals [1]. One could expect that performing LP using a model order that is twice the number of tonal components leads to a signal estimate in which each of the spectral peaks is modeled with a complex conjugate pole pair close to (but inside) the unit circle This does not EURASIP Journal on Audio, Speech, and Music Processing seem to be the case, and very often a poor LP signal estimate is obtained. All considered approaches result in stable LP models, and some outperform the WLP model both in terms of conventional measures, such as frequency estimation error and residual spectral flatness [43, Chapter 6], and in terms of perceptually motivated measures, such as interpeak dip depth (IDD) [12] Many of these alternative models perform even better when cascaded with a conventional LP model.
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