On the Design and Implementation of Higher Order Differential Microphones

A novel systematic approach to the design of directivity patterns of higher order differential microphones is proposed. The directivity patterns are obtained by optimizing a cost function which is a convex combination of a front-back energy ratio and uniformity within a frontal sector of interest. Most of the standard directivity patterns - omnidirectional, cardioid, subcardioid, hypercardioid, supercardioid - are particular solutions of this optimization problem with specific values of two free parameters: the angular width of the frontal sector and the convex combination factor. More general solutions of practical use are obtained by varying these two parameters. Many of these optimal directivity patterns are trigonometric polynomials with complex roots. A new differential array structure that enables the implementation of general higher order directivity patterns, with complex or real roots, is then proposed. The effectiveness of the proposed design framework and the implementation structure are illustrated by design examples, simulations, and measurements.

[1]  Ronald D. Streicher,et al.  The Bidirectional Microphone: A Forgotten Patriarch , 2003 .

[2]  Walter Kellermann,et al.  Design of robust superdirective beamformers as a convex optimization problem , 2009, 2009 IEEE International Conference on Acoustics, Speech and Signal Processing.

[3]  Michael S. Brandstein,et al.  Microphone Arrays - Signal Processing Techniques and Applications , 2001, Microphone Arrays.

[4]  P. Stoica,et al.  Robust Adaptive Beamforming , 2013 .

[5]  Mohamad Adnan Al-Alaoui,et al.  Novel digital integrator and differentiator , 1993 .

[6]  Angelo Farina,et al.  Simultaneous Measurement of Impulse Response and Distortion with a Swept-Sine Technique , 2000 .

[7]  Gary W. Elko,et al.  Differential Microphone Arrays , 2004 .

[8]  Christof Faller,et al.  Spatiotemporal Gradient Analysis of Differential Microphone Arrays , 2009 .

[9]  Boaz Rafaely,et al.  Phase-mode versus delay-and-sum spherical microphone array processing , 2005, IEEE Signal Processing Letters.

[10]  A. T. Parsons,et al.  Maximum directivity proof for three‐dimensional arrays , 1987 .

[11]  Thushara D Abhayapala,et al.  Higher order differential-integral microphone arrays. , 2010, The Journal of the Acoustical Society of America.

[12]  Gary W. Elko,et al.  Microphone array systems for hands-free telecommunication , 1996, Speech Commun..

[13]  Shefeng Yan,et al.  Robust spherical microphone array beamforming with multi-beam-multi-null steering, and sidelobe control , 2009, 2009 IEEE Workshop on Applications of Signal Processing to Audio and Acoustics.

[14]  Zoran Cvetkovic,et al.  A generalized design method for directivity patterns of spherical microphone arrays , 2011, 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[15]  Unto K. Laine,et al.  Splitting the unit delay [FIR/all pass filters design] , 1996, IEEE Signal Process. Mag..

[16]  Zoran Cvetkovic,et al.  Design of a Circular Microphone Array for Panoramic Audio Recording and Reproduction: Microphone directivity , 2010 .

[17]  Jacob Benesty,et al.  Audio Signal Processing for Next-Generation Multimedia Communication Systems , 2004 .

[18]  R. Marshall,et al.  New Microphone Providing Uniform Directivity Over an Extended Frequency Range , 1939 .

[19]  HamacherV.,et al.  Signal processing in high-end hearing aids , 2005 .

[20]  Boaz Rafaely.  Design of a Second-Order Soundfield Microphone , 2005 .

[21]  Gary W. Elko,et al.  A highly scalable spherical microphone array based on an orthonormal decomposition of the soundfield , 2002, 2002 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[22]  Michio Matsumoto,et al.  Stereo zoom microphone for consumer video cameras , 1989 .

[23]  G. Sessler,et al.  Directional transducers , 1971 .

[24]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[25]  Walter Kellermann,et al.  Towards Natural Acoustic Interfaces for Automatic Speech Recognition , 2009 .

[26]  Marc Moonen,et al.  Design of broadband beamformers robust against gain and phase errors in the microphone array characteristics , 2003, IEEE Trans. Signal Process..

[27]  Thushara D. Abhayapala,et al.  Theory and design of high order sound field microphones using spherical microphone array , 2002, 2002 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[28]  Mohamad Adnan Al-Alaoui,et al.  Using fractional delay to control the magnitudes and phases of integrators and differentiators , 2007 .

[29]  Henning Puder,et al.  Signal Processing in High-End Hearing Aids: State of the Art, Challenges, and Future Trends , 2005, EURASIP J. Adv. Signal Process..