An automatic design procedure for low-order IIR parametric equalizers

Parametric equalization of an acoustic system aims to compensate for the deviations of its response from a desired target response using parametric digital filters. An optimization procedure is presented for the automatic design of a low-order equalizer using parametric infinite impulse response (IIR) filters, specifically second-order peaking filters and first-order shelving filters. The proposed procedure minimizes the sum of square errors (SSE) between the system and the target complex frequency responses, instead of the commonly used difference in magnitudes, and exploits a previously unexplored orthogonality property of one particular type of parametric filter. This brings a series of advantages over the state-of-the-art procedures, such as an improved mathematical tractability of the equalization problem, with the possibility of computing analytical expressions for the gradients, an improved initialization of the parameters, including the global gain of the equalizer, the incorporation of shelving filters in the optimization procedure, and a more accentuated focus on the equalization of the more perceptually relevant frequency peaks. Examples of loudspeaker and room equalization are provided, as well as a note about extending the procedure to multi-point equalization and transfer function modeling

Sparse linear parametric modeling of room acoustics with orthonormal basis functions

© 2014 EURASIP. Orthonormal Basis Function (OBF) models provide a stable and well-conditioned representation of a linear system. When used for the modeling of room acoustics, useful information about the true dynamics of the system can be introduced by a proper selection of a set of poles, which however appear non-linearly in the model. A novel method for selecting the poles is proposed, which bypass the non-linear problem by exploiting the concept of sparsity and by using convex optimization. The model obtained has a longer impulse response compared to the all-zero model with the same number of parameters, without introducing substantial error in the early response. The method also allows to increase the resolution in a specified frequency region, while still being able to approximate the spectral envelope in other regions.status: publishe

An automatic model-building algorithm for sparse approximation of room impulse responses with orthogonal basis functions

© 2014 IEEE. Orthonormal Basis Function (OBF) models are used to define stable fixed-poles infinite impulse response filter structures that allow to incorporate knowledge about the resonant characteristics of a stable, causal and linear system. In the approximation of a room impulse response, OBF models can include knowledge about the room resonances as a set of poles, which appear nonlinearly in the structure. A novel algorithm is pro-posed, that avoids this nonlinear problem by iteratively estimating the poles and building the model. Some of the properties of OBF models, such as orthogonality and linearity-in-the-parameters, are exploited and the final model has the favorable property of being scalable. The OBF model provides a longer response than the all-zero model and is particularly suited in approximating the early response and the predominant resonances for relatively small model orders.status: publishe

Room acoustic system identification using orthonormal basis function models'

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A scalable algorithm for physiclly motivated and sparse approximation of room impulse responses with orthonormal basis functions

© 2014 IEEE. Parametric modeling of room acoustics aims at representing room transfer functions by means of digital filters and finds application in many acoustic signal enhancement algorithms. In previous work by other authors, the use of orthonormal basis functions (OBFs) for modeling room acoustics has been proposed. Some advantages of OBF models over all-zero and pole-zero models have been illustrated, mainly focusing on the fact that OBF models typically require less model parameters to provide the same model accuracy. In this paper, it is shown that the orthogonality of the OBF model brings several additional advantages, which can be exploited if a suitable algorithm for identifying the OBF model parameters is applied. Specifically, the orthogonality of OBF models does not only lead to improved model efficiency (as pointed out in previous work), but also leads to improved model scalability and model stability. Its appealing scalability property derives from a previously unexplored interpretation of the OBF model as an approximation to a solution of the inhomogeneous acoustic wave equation. Following this interpretation, a novel identification algorithm is proposed that takes advantage of the OBF model orthogonality to deliver efficient, scalable, and stable OBF model estimates, which is not necessarily the case for nonlinear estimation techniques that are normally applied.status: publishe