A linear phase IIR filterbank for the radial filters of ambisonic recordings
Résumé
Higher order Ambisonics decomposition of natural sound fields is often performed using spherical, rigid microphone array measurements, mainly because of its simple implementation[1-2]. All the electronic equipment can be conveniently placed inside the spherical measurement array, without affecting the scattered acoustic field. However, restitution systems for HOA sound field synthesis generally exhibit a much larger radius than measurement arrays. The well-known “bass-boost” effect is directly linked to this size discrepancy: low frequencies have to be amplified, especially for higher order components of the Ambisonics decomposition. The dynamic range for filtering purposes is limited, mainly by the signal-to-noise ratio of the microphone array. In order to overcome this problem, we developed two microphone array prototypes using analogic MEMS microphones, which have become a viable solution in a small packaging and with a reasonable price thanks to the growing use of these sensors in domotics and in the mobile phone industry. MEMS microphones from the same production batch exhibit very similar characteristics and can be used for array signal processing without any level or phase calibration. The two proposed prototypes are made of group of 4 MEMS microphones for the same sensor position to improve the signal-to-noise ratio by 6 dB. The first prototype is a 5-th order Ambisonics system (50 sensors – 200 mems – lie on a Lebedev grid) and the second prototype is a Mixed Order Ambisonics (MOA) system (42 sensors – 168 mems – 3-th order in 3D and 11-th order in 2D, 24 sensors in the equator of the sphere) [3].Nevertheless, this approach does not dispense from the need to filter higher order coefficients. A simple high-pass filtering on each order component is not sufficient, since this would not only cause losses in terms of amplitude and power but also would affect the loudness of the restitution. A filter bank is therefore needed to cut-off noise amplification at low frequencies and apply appropriate gains for loudness equalization. Baumgartner and al [4] proposed a non-linear phase filter bank based on Linkwitz-Riley IIR filters. In order to avoid group delay distortions, Zotter proposed a linear phase filter bank based on FIR filters and the use of fast block convolution [5]. This solution is although not very flexible, since the FIR strongly depend on the radius of the measurement array and on the filter bank’s cut-off frequencies. Any change in the measurement system require a new computation of each FIR filters corresponding. In the present paper, a linear phase IIR filter bank is implemented. Thanks to the use of local overlap and add time reversal blocks [6], the filter bank exhibits a linear phase delay which only depends on the time reversal blocksize. The proposed implementation of the filter bank allows to change in real-time the frequency bands and loudness equalization (diffuse or free field equalization) using of Faust programming language [7].[1] S. Bertet, J. Daniel, E. Parizet, L. Gros, and O. Warusfel, “Investigation of the perceived spatial resolution of higher order ambisonics sound fields: a subjective evaluation involving virtual and real 3D microphones”, AES 30th International Conference, Saariselkä, Finland, 2007 March 15–17.[2] J. Meyer and G. Elko, “A highly scalable spherical microphone array based on an orthonormal decomposition of the soundfield,” in Acoustics, Speech, and Signal Processing, 2002. Proceedings.(ICASSP’02). IEEE International Conference on, vol. 2, Orlando, FL, USA, 2002.[3] S. Favrot, M. Marschall , J. Käsbach , J. Buchholz, T. Weller, “Mixed-order Ambisonics recording and playback for improving horizontal directionality”, presented at the AES 131st convention, New York, USA, 2011. [4] R. Baumgartner, H. Pomberger, and M. Frank, “Practical Implementation of Radial Filters for Ambisonic Recordings”, in Proc. first International Conference on Spatial Audio, Detmold, Germany, 2011.[5] F. Zotter, “A Linear-Phase Filter-Bank Approach to Process Rigid Spherical Microphone Array Recordings”, Proceedings of Papers – 5th International Conference on Electrical, Electronic and Computing Engineering, IcETRAN 2018, Palić, Serbia, June 11 – 14, 2018[6] S.R Powell and P.M Chau, “A technique for realizing linear phase IIR filter”, IEEE transactions and signal processing, vol 29(11), november 1991, 2425-2435.[7] For Faust programming language, see https://faust.grame.fr/
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