Francesca Ortolani

A new approach to acoustic beamforming from virtual microphones based on ambisonics for adaptive noise cancelling

Interference in three-dimensional audio systems is a problematic issue. Eliminating noise, or any other disturbing source, without affecting the spatial audio rendering, is challenging, indeed. Using the least possible number of microphone capsules and reduced size is another issue. An elementary way for accomplishing this job makes use of a 3D audio technique called Ambisonics and a coincident microphone array of 4 elements. This technique allows shaping cardioid-like virtual microphones pointing to a jamming source. This disturbing signal can be used to feed an adaptive noise canceller and kill noise from the 3D recording. Evidently, a 4-capsule array extracts cardioids up to first order. The final result can be improved if microphones with higher directivity are employed. This paper presents a method for deriving highly-directive virtual microphones by means of a 4-capsule ambisonic array and spaced virtual capsules.

Frequency domain quaternion adaptive filters

Recently, adaptive filtering was extended to quaternion-valued systems. Quaternion-valued algorithms exhibit improved geometrical properties compared with real- and complex-valued algorithms. Moreover, working in the frequency domain allows a fast execution along with a good convergence performance. In this work, we propose three different quaternion-valued adaptive algorithms operating in the frequency domain. Convergence properties are also analyzed: in particular, the step size stability range is obtained in relation to the eigenvalues of the input autocorrelation matrix and the Excess Mean Square Error (EMSE) is expressed in relation to the algorithm parameters. Finally, simulations support the proposal.

The widely linear block quaternion least mean square algorithm for fast computation in 3D audio systems

In this paper we propose an algorithm which operates weight adaptation by means of a periodic law and is based on the Widely Linear Quaternion Least Mean Square (WL-QLMS) algorithm. The WL-QLMS successfully handles real-world signals, either proper or improper. However, because of the introduction of full second order statistics into the algorithm, its computational cost is quadruplicated with respect to its precursor QLMS. The proposed Widely Linear Block Quaternion Least Mean Square (WL-BQLMS) algorithm speeds up the execution, thus revealing itself as a good solution in 3D audio signal processing applications, where huge amounts of data are usually treated and signals are typically improper. Simulations exploiting 3D Ambisonic B-Format audio signals provide a report of the WL-BQLMS behavior in comparison with BQLMS.

Widely linear quaternion adaptive filtering in the frequency domain

Adaptive filtering can be expanded to new numerical systems and unseen sides of physical problems can be highlighted thanks to the mathematical properties of such hypercomplex algebras. Each algebra has its own rules and operation results may not be compatible from one algebra to another. However, such peculiarities diversify algebras in a way that each of them fits specific geometrical/physical problems. In this work we propose a quaternion widely linear adaptive algorithm operating in the frequency domain. The aim is to overcome the problem of high computational cost occurring when time-domain algorithms are used. An analysis of the cost is also supplied. Finally, simulations support our proposal.

On 4-Dimensional Hypercomplex Algebras in Adaptive Signal Processing

The degree of diffusion of hypercomplex algebras in adaptive and non-adaptive filtering research topics is growing faster and faster. The debate today concerns the usefulness and the benefits of representing multidimensional systems by means of these complicated mathematical structures and the criterions of choice between one algebra or another. This paper proposes a simple comparison between two isodimensional algebras (quaternions and tessarines) and shows by simulations how different choices may determine the system performance. Some general information about both algebras is also supplied.

Advances in hypercomplex adaptive filtering for 3D audio processing

3-dimensional (3D) audio is the new frontier in audio technology and it is quickly taking place in many applications, from cinema to virtual reality, audio surveillance and video games. The large amount of data requires fast and compact solutions for signal processing. With this aim in view, research is moving towards the exploration of hypercomplex algebras in order to find a non-redundant and compact form for the representation of 3D audio sound fields without the loss of information. Quaternion sound fields are currently under investigation and this paper presents some recent results in adaptive signal processing for quaternion 3D audio.

Quaternion digital signal processing: A hypercomplex approach to information processing

During the recent years, signal processing research started investigating hypercomplex numbers and their usefulness in the modeling of systems. Together, digital signal processing groups started developing multidimensional algorithms in the hypercomplex domains. At present, many proposals include quaternion, octonion and Lie algebra solutions. However, a canonical definition of discrete-time hypercircuit has not been written, yet. This paper has the aim to strengthen the concept of discrete-time hypercircuit theory. In addition, we intend to give a definition of quaternion convolution and Z-Transform in an established form. Besides this, filter design examples and simulations from the adaptive filtering context are supplied.

Frequency-Domain Adaptive Filtering in Hypercomplex Systems

In recent years, linear and nonlinear signal processing applications required the development of new multidimensional algorithms. Higher-dimensional algorithms include quaternion-valued filters. One of the drawbacks filter designers have to cope with is the increasing computational cost due to multidimensional processing. A strategy to reduce the computational complexity of long adaptive filters is to implement block algorithms and update the filter coefficients periodically. More efficient techniques embed frequency-domain processing in block algorithms with the use of the Fast Fourier Transform (FFT). Transform-domain adaptive filters in the quaternion field require quaternion-valued transforms. In this paper we also suggest a simple method to obtain a quaternionic DFT/FFT from a complex DFT/FFT. As an example, we propose the Overlap-Save Quaternion Frequency Domain algorithm.

On the Influence of Microphone Array Geometry on the Behavior of Hypercomplex Adaptive Filters

The performance of hypercomplex adaptive filters has been widely experimented during the last decade. Quaternion filters, especially, have been utilized in systems where the signals to be processed have some form of correlation. However, besides correlation, some resolved explanation about what particular algebra to use in a certain context has not been provided, yet. This work tries to contribute in this direction by proposing an experiment that puts filters to the test with changing the input signal geometry. The tests presented in this paper take place in acoustic environment and show how a proper sound space transformation, along with the choice of the mathematical format for processing, can improve a filter performance.

On the implementation of audio envelope generators with memristor-based circuits

The Memristor is considered as the fourth fundamental element besides the resistor, the capacitor and the inductor. When Leon Chua first introduced this element, it was just a theoretical idea. Today, after 30 years from Chuas first paper about it, it is possible to buy memristor devices. In this paper, we investigate a way to exploit memristors in a typical audio application: the implementation of envelope generators. It is possible to exploit the delayed switching property of memristors to realize long delays without the need of big capacitors. We present the implementation of a ramp generator by means of a memristor-based circuit. The ramp signal can be used as control signal in an audio device.