In this paper, we propose a data-driven approach for the reconstruction of unknown room impulse responses (RIRs) based on the deep prior paradigm. We formulate RIR reconstruction as an inverse problem. More specifically, a convolutional neural network (CNN) is employed prior, in order to obtain a regularized solution to the RIR reconstruction problem for uniform linear arrays. This approach allows us to avoid assumptions on sound wave propagation, acoustic environment, or measuring setting made in state-of-the-art RIR reconstruction algorithms. Moreover, differently from classical deep learning solutions in the literature, the deep prior approach employs a per-element training. Therefore, the proposed method does not require training data sets, and it can be applied to RIRs independently from available data or environments. Results on simulated data demonstrate that the proposed technique is able to provide accurate results in a wide range of scenarios, including variable direction of arrival of the source, room ${\mathrm{T}}_{60}$, and SNR at the sensors. The devised technique is also applied to real measurements, resulting in accurate RIR reconstruction and robustness to noise compared to state-of-the-art solutions.

We present a spatial filtering approach to first-order steerable Differential Microphone Arrays (DMAs) with arbitrary planar geometry. In particular, the design of the spatial filter is based on a recently proposed frequency-domain design methodology that approximates, in a least-square sense, a target beampattern using the Jacobi-Anger expansion involving Bessel functions. Despite the generality of that approach, however, its computational cost turns out to be excessive when working with limited processing resources. The beamforming technique proposed in this manuscript overcomes this issue by exploiting the fact that in DMAs the spacing between sensors is typically smaller than the smallest wavelength of audio signals of interest. This allows us to substitute zero- and first-order Bessel functions with their Taylor series approximation truncated to the first order. Moreover, we show that this approximation allows us to derive an efficient discrete-time-domain implementation of first-order steerable differential beamformers based on arrays with arbitrary geometries.

Performing continuous beam steering, from planar arrays of high-order differential microphones, is not trivial. The main problem is that shape-preserving beams can be steered only in a finite set of privileged directions, which depend on the position and the number of physical microphones. In this letter, we propose a simple and computationally inexpensive method for alleviating this problem using planar microphone arrays. Given two identical reference beams pointing in two different directions, we show how to build a beam of nearly constant shape, which can be continuously steered between such two directions. The proposed method, unlike the diffused steering approaches based on linear combinations of eigenbeams (spherical harmonics), is applicable to planar arrays also if we deal with beams characterized by high-order polar patterns. Using the coefficients of the Fourier series of the polar patterns, we also show how to find a tradeoff between shape invariance of the steered beam, and maximum angular displacement between the two reference beams. We show the effectiveness of the proposed method through the analysis of models based on first-, second-, and third-order differential microphones.

The wave digital filter (WDF) technique derives digital filters from analog prototypes that classically have been restricted to passive circuits with series/parallel topologies. Since most audio circuits contain active elements (e.g., op-amps) and complex topologies, WDFs have only had limited use in virtual analog modeling. In this paper, we extend the WDF approach to accommodate the unbounded class of non-series/parallel junctions which may absorb linear multiports. We present four modified-nodal-analysis-based scattering matrix derivations for these junctions, using parametric waves with voltage, power, and current waves as particular cases. Three derivations afford implementations whose cost in multiplies are lower than multiplying by the scattering matrix. Negative port resistances may be needed in WDF modeling of active circuits, restricting the WDF to voltage or current waves. We propose two techniques for localizing this restriction. Case studies on the Baxandall tone circuit and a ``Frequency Booster'' guitar pedal demonstrate the proposed techniques in action.

We propose a spatial filtering method for linear arrays of First-Order Steerable Differential Microphones (FOSDMs), which operates in two layers. In the former, signals acquired by individual microphones are locally filtered to produce the outputs of the FOSDMs. In the latter, the outputs of the FOSDMs are processed by another filter. We analyse different design methodologies and study the conditions under which the two filtering layers can be decoupled. The proposed two-layer spatial filter can be flexibly controlled with a single scalar parameter, which can be chosen, for example, to maximize the White Noise Gain (like in a Delay-and-Sum beamformer); or to maximize the Directivity Factor (like in a Super-Directive beamformer); without needing any matrix inversion. The effectiveness of the proposed beamforming method is compared with traditional spatial filtering techniques using different metrics.

A large class of transcendental equations involving exponentials can be made explicit using the Lambert W function. In the last fifteen years, this powerful mathematical tool has been extensively used to find closed-form expressions for currents or voltages in circuits containing diodes. Until now almost all the studies about the W function in circuit analysis concern the Kirchhoff (K) domain, while only few works in the literature describe explicit models for diode circuits in the Wave Digital (WD) domain. However explicit models of NonLinear Elements (NLEs) in the WD domain are particularly desirable, especially in order to avoid the use of iterative algorithms. This paper explores the range of action of the W function in the WD domain; it describes a procedure to search for explicit wave mappings, for both one-port and multi-port NLEs containing diodes. WD models, describing an arbitrary number of different parallel and anti-parallel diodes, a transformerless ring modulator and some BJT amplifier configurations, are derived. In particular, an extended version of the BJT Ebers-Moll model, suitable for implementing feedback between terminals, is introduced.