A Kalman-based Fundamental Frequency Estimation Algorithm

Fundamental frequency estimation is an important task in speech and audio analysis. Harmonic model-based methods typically have superior estimation accuracy. However, such methods usually as- sume that the fundamental frequency and amplitudes are station- ary over a short time frame. In this paper, we propose a Kalman filter-based fundamental frequency estimation algorithm using the harmonic model, where the fundamental frequency and amplitudes can be truly nonstationary by modeling their time variations as first- order Markov chains. The Kalman observation equation is derived from the harmonic model and formulated as a compact nonlinear matrix form, which is further used to derive an extended Kalman filter. Detailed and continuous fundamental frequency and ampli- tude estimates for speech, the sustained vowel /a/ and solo musical tones with vibrato are demonstrated

Sparse Semi-Parametric Estimation of Harmonic Chirp Signals

In this work, we present a method for estimating the parameters detailing an unknown number of linear, possibly harmonically related, chirp signals, using an iterative sparse reconstruction framework. The proposed method is initiated by a re-weighted group-sparsity approach, followed by an iterative relaxation-based refining step, to allow for high resolution estimates. Numerical simulations illustrate the achievable performance, offering a notable improvement as compared to other recent approaches. The resulting estimates are found to be statistically efficient, achieving the corresponding Cram´er-Rao lower bound