Infinite kernel linear prediction for joint estimation of spectral envelope and fundamental frequency

This paper presents a new probabilistic formulation of linear prediction (LP) for jointly estimating the spectral envelope and fundamental frequency (F0) of a speech signal. A main problem of classical LP is that the peaks of the estimated envelope are highly biased toward the harmonic partials of a speech spectrum. To solve this problem, we propose a nonparametric Bayesian model called infinite kernel linear prediction (IKLP) based on a Gaussian process with multiple kernel learning. Our model can represent the periodicity of a speech signal by using a weighted sum of infinitely many periodic kernels that correspond to different F0s. We put a gamma process prior on the positive weights of those kernels and perform sparse learning to determine a predominant kernel indicating the F0 at the same time of spectral envelope estimation. The experimental results showed that our model can estimate spectral envelopes and F0s of speech and singing signals while identifying pitched segments.