Paper Archive

In designing a frequency tracker, the goal is to follow the continual time variation of the frequency from a particular sinusoidal component in a noisy signal with a high accuracy and a low sample delay. Although there exists a plethora of frequency trackers in the literature, in this paper, we focus on the particular class of frequency trackers that are built upon an adaptive notch filter (ANF), i.e. a constrained bi-quadratic infinite impulse response filter, where only a single parameter needs to be estimated. As opposed to using the conventional least-mean-square (LMS) algorithm, we present an alternative approach for the estimation of this parameter, which ultimately corresponds to the frequency to be tracked. Specifically, we reformulate the ANF in terms of a state-space model, where the state contains the unknown parameter and can be subsequently updated using a Kalman filter. We also demonstrate that such an approach is equivalent to doing a normalized LMS filter update, where the regularization parameter can be expressed as the ratio of the variance of the measurement noise to the variance of the prediction error. Through an evaluation with both simulated and realistic data, it is shown that in comparison to the LMS-updated frequency tracker, the proposed Kalmanupdated alternative, results in a more accurate performance, with a faster convergence rate, while maintaining a low computational complexity and the ability to be updated on a sample-by-sample basis.

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In rooms with complex geometry and uneven distribution of energy losses, late reverberation depends on the positions of sound sources and listeners. More precisely, the decay of energy is characterised by a sum of exponential curves with position-dependent amplitudes and position-independent decay rates (hence the name common slopes). The amplitude of different energy decay components is a particularly important perceptual aspect that requires efficient modeling in applications such as virtual reality and video games. Acoustic Radiance Transfer (ART) is a room acoustics model focused on late reverberation, which uses a pre-computed acoustic transfer matrix based on the room geometry and materials, and allows interactive changes to source and listener positions. In this work, we present an efficient common-slopes approximation of the ART model. Our technique extracts common slopes from ART using modal decomposition, retaining only the non-oscillating energy modes. Leveraging the structure of ART, changes to the positions of sound sources and listeners only require minimal processing. Experimental results show that even very few slopes are sufficient to capture the positional dependency of late reverberation, reducing model complexity substantially.

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