Damped Chirp Mixture Estimation via Nonlinear Bayesian Regression
Estimating mixtures of damped chirp sinusoids in noise is a
problem that affects audio analysis, coding, and synthesis applications. Phase-based non-stationary parameter estimators assume
that sinusoids can be resolved in the Fourier transform domain,
whereas high-resolution methods estimate superimposed components with accuracy close to the theoretical limits, but only for
sinusoids with constant frequencies. We present a new method
for estimating the parameters of superimposed damped chirps that
has an accuracy competitive with existing non-stationary estimators but also has a high-resolution like subspace techniques. After providing the analytical expression for a Gaussian-windowed
damped chirp signal’s Fourier transform, we propose an efficient
variational EM algorithm for nonlinear Bayesian regression that
jointly estimates the amplitudes, phases, frequencies, chirp rates,
and decay rates of multiple non-stationary components that may be
obfuscated under the same local maximum in the frequency spectrum. Quantitative results show that the new method not only has
an estimation accuracy that is close to the Cramér-Rao bound, but
also a high resolution that outperforms the state-of-the-art.