Download 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.
Download On the Estimation of Sinusoidal Parameters via Parabolic Interpolation of Scaled Magnitude Spectra 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 HD-AD: A New Approach to Audio Atomic Decomposition with Hyperdimensional Computing In this paper, we approach the problem of atomic decomposition of audio at the symbolic level of atom parameters through the lens of hyperdimensional computing (HDC) – a non-traditional computing paradigm. Existing atomic decomposition algorithms often operate using waveforms from a redundant dictionary of atoms causing them to become increasingly memory/computationally intensive as the signal length grows and/or the atoms become more complicated. We systematically build an atom encoding using vector function architecture (VFA), a field of HDC. We train a neural network encoder on synthetic audio signals to generate these encodings and observe that the network can generalize to real recordings. This system, we call Hyperdimensional Atomic Decomposition (HD-AD), avoids time-domain correlations all together. Because HD-AD scales with the sparsity of the signal, rather than its length in time, atomic decompositions are often produced much faster than real-time.
Download Hybrid Audio Inpainting Approach with Structured Sparse Decomposition and Sinusoidal Modeling This research presents a novel hybrid audio inpainting approach that considers the diversity of signals and enhances the reconstruction quality. Existing inpainting approaches have limitations, such as energy drop and poor reconstruction quality for non-stationary signals. Based on the fact that an audio signal can be considered as a mixture of three components: tonal, transients, and noise, the proposed approach divides the left and right reliable neighborhoods around the gap into these components using a structured sparse decomposition technique. The gap is reconstructed by extrapolating parameters estimated from the reliable neighborhoods of each component. Component-targeted methods are refined and employed to extrapolate the parameters based on their own acoustic characteristics. Experiments were conducted to evaluate the performance of the hybrid approach and compare it with other stateof-the-art inpainting approaches. The results show the hybrid approach achieves high-quality reconstruction and low computational complexity across various gap lengths and signal types, particularly for longer gaps and non-stationary signals.