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.

Download

Sinusoids are widely used to represent the oscillatory modes of music and speech. The estimation of the sinusoidal parameters directly affects the quality of the representation. A parabolic interpolation of the peaks of the log-magnitude spectrum is commonly used to get a more accurate estimation of the frequencies and the amplitudes of the sinusoids at a relatively low computational cost. Recently, Werner and Germain proposed an improved sinusoidal estimator that performs parabolic interpolation of the peaks of a power-scaled magnitude spectrum. For each analysis window type and size, a power-scaling factor p is pre-calculated via a computationally demanding heuristic. Consequently, the powerscaling estimation method is currently constrained to a few tabulated power-scaling factors for pre-selected window sizes, limiting its practical applications. In this article, we propose a method to obtain the power-scaling factor p for any window size from the tabulated values. Additionally, we investigate the impact of zeropadding on the estimation accuracy of the power-scaled sinusoidal parameter estimator.

Download