Carlo Magi

Stabilised weighted linear prediction

Weighted linear prediction (WLP) is a method to compute all-pole models of speech by applying temporal weighting of the square of the residual signal. By using short-time energy (STE) as a weighting function, this algorithm was originally proposed as an improved linear predictive (LP) method based on emphasising those samples that fit the underlying speech production model well. The original formulation of WLP, however, did not guarantee stability of all-pole models. Therefore, the current work revisits the concept of WLP by introducing a modified short-time energy function leading always to stable all-pole models. This new method, stabilised weighted linear prediction (SWLP), is shown to yield all-pole models whose general performance can be adjusted by properly choosing the length of the STE window, a parameter denoted by M. The study compares the performances of SWLP, minimum variance distortionless response (MVDR), and conventional LP in spectral modelling of speech corrupted by additive noise. The comparisons were performed by computing, for each method, the logarithmic spectral differences between the all-pole spectra extracted from clean and noisy speech in different segmental signal-to-noise ratio (SNR) categories. The results showed that the proposed SWLP algorithm was the most robust method against zero-mean Gaussian noise and the robustness was largest for SWLP with a small M-value. These findings were corroborated by a small listening test in which the majority of the listeners assessed the quality of impulse-train-excited SWLP filters, extracted from noisy speech, to be perceptually closer to original clean speech than the corresponding all-pole responses computed by MVDR. Finally, SWLP was compared to other short-time spectral estimation methods (FFT, LP, MVDR) in isolated word recognition experiments. Recognition accuracy obtained by SWLP, in comparison to other short-time spectral estimation methods, improved already at moderate segmental SNR values for sounds corrupted by zero-mean Gaussian noise. For realistic factory noise of low pass characteristics, the SWLP method improved the recognition results at segmental SNR levels below 0dB.

Closed phase covariance analysis based on constrained linear prediction for glottal inverse filtering

Closed phase (CP) covariance analysis is a widely used glottal inverse filtering method based on the estimation of the vocal tract during the glottal CP. Since the length of the CP is typically short, the vocal tract computation with linear prediction (LP) is vulnerable to the covariance frame position. The present study proposes modification of the CP algorithm based on two issues. First, and most importantly, the computation of the vocal tract model is changed from the one used in the conventional LP into a form where a constraint is imposed on the dc gain of the inverse filter in the filter optimization. With this constraint, LP analysis is more prone to give vocal tract models that are justified by the source-filter theory; that is, they show complex conjugate roots in the formant regions rather than unrealistic resonances at low frequencies. Second, the new CP method utilizes a minimum phase inverse filter. The method was evaluated using synthetic vowels produced by physical modeling and natural speech. The results show that the algorithm improves the performance of the CP-type inverse filtering and its robustness with respect to the covariance frame position.

Effect of White-Noise Correction on Linear Predictive Coding

White-noise correction is a technique used in speech coders using linear predictive coding (LPC). This technique generates an artificial noise-floor in order to avoid stability problems caused by numerical round-off errors. In this letter, we study the effect of white-noise correction on the roots of the LPC model. The results demonstrate in analytic form the relation between the noise floor level and the stability radius of the LPC model

Glottal inverse filtering with the closed-phase covariance analysis utilizing mathematical constraints in modelling of the vocal tract

Abstract Closed-phase (CP) covariance analysis is a glottal inverse filtering method based on the estimation of the vocal tract with linear prediction (LP) during the closed phase of the vocal fold vibration cycle. Since the closed phase is typically short, the analysis is vulnerable with respect to the extraction of the covariance frame position. The present study proposes a modified CP algorithm based on imposing certain predefined values on the gains of the vocal tract inverse filter at angular frequencies of 0 and π in optimizing filter coefficients. With these constraints, vocal tract models are less prone to show false low-frequency roots. Experiments show that the algorithm improves the robustness of the CP analysis on the covariance frame position.

Fast communication: Simple proofs of root locations of two symmetric linear prediction models

This paper gives simple proofs of the root locations of two linear predictive methods: the symmetric linear prediction model and the eigenfilter model corresponding to the minimal or maximal simple eigenvalues of an autocorrelation matrix. The roots of both symmetric models are proved to lie on the unit circle. Differently from previous proofs, the approach used in the present study also shows, based on the properties of the autocorrelation sequence, that the root angles of the symmetric linear prediction model are limited to occur within a certain interval. Moreover, eigenfilters corresponding to the minimum or maximum eigenvalue of an autocorrelation matrix that have multiplicity greater than unity are also studied. It turns out that it is possible to characterise the whole space spanned by the eigenvectors corresponding to the multiple eigenvalues by a single symmetric/antisymmetric eigenvector of the principal diagonal sub-block of the autocorrelation matrix having all the roots on the unit circle.

Minimum Separation of Line Spectral Frequencies

We provide a theoretical lower limit on the distance of line spectral frequencies for both the line spectrum pair decomposition and the immittance spectrum pair decomposition. The result applies to line spectral frequencies computed from linear predictive polynomials with all roots within a zero-centered circle of radius r<1

Objective and Subjective Evaluation of Seven Selected All-Pole Modelling Methods in Processing of Noise Corrupted Speech

Spectral modeling properties of seven selected all-pole modeling methods were compared by using both objective and subjective tests. Model behavior was evaluated with vowel sounds corrupted by uncorrelated Gaussian and Laplacian background noise. Objective tests were computed with the logarithmic spectral differences (SD2) and subjective speech quality was assessed with the degradation category rating (DCR) listening test. In both tests, the WLPC method, where the weighting function was the short time energy of the speech signal, gave the best results. The correlation between the objective and subjective results was found to be remarkably strong