Thomas Dietzen

Randall Ali, Thomas Dietzen, Matteo Scerbo et al.

We introduce a new framework for room acoustics modelling based on a state-space model of the boundary integral equation representing the sound field in a room. Whereas state-space models of linear time-invariant systems are traditionally constructed by means of a state vector and a 4-tuple of system matrices, the state-space representation introduced in this work consists of a state function representing the pressure distribution at the room boundary, and a 4-tuple of integral operators. We refer to this representation as a boundary integral operator state-space (BIOSS) model and provide a physical interpretation for each of the integral operators. As many mathematical operations on vectors and matrices translate to functions and operators, the BIOSS representation can be manipulated to obtain two transfer function representations, having either a feedback or a parallel feedforward structure. Consequently, various equivalent representations for room acoustics are obtained in the BIOSS framework, in the time or frequency domain, and in continuous or discrete space. We discuss two future directions for how the proposed framework can be fertile for research on room acoustics modelling. Firstly, we identify equivalences between the BIOSS framework and various existing room acoustics models (boundary element models, delay networks, geometric models), which may be used to establish relations between existing models and to develop novel room acoustics models. Secondly, we postulate on how concepts from state-space theory, such as observability, controllability, and state realization, can be used for developing new inference and control methods for room acoustics.

Thomas Dietzen, Marc Moonen, Toon van Waterschoot

Power spectral density (PSD) estimates of various microphone signal components are essential to many speech enhancement procedures. As speech is highly non-nonstationary, performance improvements may be gained by maintaining time-variations in PSD estimates. In this paper, we propose an instantaneous PSD estimation approach based on generalized principal components. Similarly to other eigenspace-based PSD estimation approaches, we rely on recursive averaging in order to obtain a microphone signal correlation matrix estimate to be decomposed. However, instead of estimating the PSDs directly from the temporally smooth generalized eigenvalues of this matrix, yielding temporally smooth PSD estimates, we propose to estimate the PSDs from newly defined instantaneous generalized eigenvalues, yielding instantaneous PSD estimates. The instantaneous generalized eigenvalues are defined from the generalized principal components, i.e. a generalized eigenvector-based transform of the microphone signals. We further show that the smooth generalized eigenvalues can be understood as a recursive average of the instantaneous generalized eigenvalues. Simulation results comparing the multi-channel Wiener filter (MWF) with smooth and instantaneous PSD estimates indicate better speech enhancement performance for the latter. A MATLAB implementation is available online.

Thomas Dietzen, Enzo De Sena, Toon van Waterschoot

The steered response power (SRP) approach to acoustic source localization computes a map of the acoustic scene from the frequency-weighted output power of a beamformer steered towards a set of candidate locations. Equivalently, SRP may be expressed in terms of time-domain generalized cross-correlations (GCCs) at lags equal to the candidate locations' time-differences of arrival (TDOAs). Due to the dense grid of candidate locations, each of which requires inverse Fourier transform (IFT) evaluations, conventional SRP exhibits a high computational complexity. In this paper, we propose a low-complexity SRP approach based on Nyquist-Shannon sampling. Noting that on the one hand the range of possible TDOAs is physically bounded, while on the other hand the GCCs are bandlimited, we critically sample the GCCs around their TDOA interval and approximate the SRP map by interpolation. In usual setups, the number of sample points can be orders of magnitude less than the number of candidate locations and frequency bins, yielding a significant reduction of IFT computations at a limited interpolation cost. Simulations comparing the proposed approximation with conventional SRP indicate low approximation errors and equal localization performance. MATLAB and Python implementations are available online.