Notes

Outline

Computer simulation of Binaural, Stereo-Dipole, B-format and Ambiophonics impulse responses Angelo Farina (1), Lamberto Tronchin (2) (1) Industrial Engineering Dept., University of Parma, Via delle Scienze 181/A 43100 Parma, ITALY – HTTP://pcfarina.eng.unipr.it (2) DIENCA-CIARM, University of Bologna, Via Risorgimento 42 40136 Bologna, Italy – HTTP://ciarm.ing.unibo.it

Goals This paper describes the processing required for obtaining a realistic audible sound reproduction from the results of a geometrical room acoustics program This overall process is usually known as “Auralization”, and traditionally is performed through the binaural technology (headphone reproduction) Here the process is generalized to many more reproduction systems: Mono, Binaural, Stereo Dipole, Ambisonics and Ambiophonics. The last three systems are loudspeaker-based

Methods In all these 5 cases, anyway, the auralization is obtained by means of real-time convolution of dry signals with properly derived impulse responses Convolution is now possible in real time, with many simultaneous channels, directly on a low cost PC without any added hardware, thanks to available free sofware, which outperforms traditional DSP-based convolvers Consequently, this paper focuses on the derivation of the proper sets of impulse responses for each reproduction method, starting from the results of the geometrical room acoustic program.

Processing path of the results of a geometrical room acoustic simulation

Software convolvers The multichannel convolution can be done for free on a low cost PC nowadays. Two solutions are currently available:

The conversion routine This piece of software has to read the result files produced by the room acoustics simulation program (Ramsete 2), and process them for deriving a multichannel set of impulse responses, corresponding to those which could be recorded experimentally in a real hall employing a multichannel microphone of the chosen kind. Actually the Audio Converter program developed for the release version of Ramsete 2 supports these microphonic standards: Coincident spherical harmonics (mono, 1st and 2nd order Ambisonics), Binaural (Kemar), Stereo-Dipole (Kemar), Dual Stereo Dipole (Kemar), Ambiophone (Pinnaless sphere dummy head)

Combination of multiple sources Ramsete can combine the results of several sound sources emitting the same signal, with optional delay and equalization (multi-source sound reinforcement systems):

Results from the Ramsete program In each receiver point, Ramsete computes an energetic impulse response in ten octave bands for each sound source (or combination of multiple sources):

Detail of the initial part of the IR The temporal density of the reflections initially grows (theoretically with the square of time), but later it starts reducing and eventually vanishes.

Rationale of the conversion process First the discrete early reflections are processed, taking into account their known arrival direction and exact timing. For each discrete arrival, a Dirac’s delta is generated at the exact arrival time, then it is convolved with the impulse response of an octave-band equalizer which imposes the proper SPL value in the 10 octave bands, and finally it is convolved with the multichannel impulse response of the selected type of microphone, chosen depending on the direction of arrival.

Reference system definition A local cartesian reference system is assumed solidal with the listener head; X’ axis is pointing forward (nose), Y’axis is pointing on the left ear, and the Z’ axis towards the top of the head.

Conversion formulas between absolute points and local angles The Ramsete program saves the coordinates of three points in the absolute reference system: - Pprov º  (xprov, xprov, xprov) =  provenience point of the ray; - Orec º (xrec, yrec, zrec) =  receiver origin; - Ptarg º (xt, yt, zt) = receiver target point. First of all, the position of the provenience point of the ray is recomputed in the local reference system: Pprov º> P’prov (x’prov, y’prov, z’prov)

Conversion formulas between absolute points and local angles Elevation angle j : Azimuth angle q :

Ambisonics Impulse Responses 0th Order can be listened to through a single loudspeaker 1st and 2nd orders must be properly matrixed, for driving an Ambisonics array of loudspeakers surrounding the listener

Ambisonics decoding Hardware decoders are obsolete nowadays. Free software is available for 1st and 2nd order real-time decoding, driving a multichannel sound board (thanks to Richard Furse) The decoding structure can be realized also by means of a multichannel convolution software (BruteFir, Ambiovolver, FIRreverb)

Binaural impulse responses In Ambisonics, the directive microphones IRs are simply matter of changing the gain (and perhaps the polarity) of a Dirac’s delta function In the binaural case, instead, a complex stereo IR is required for any direction-of-arrival A large data base of stereo binaural IRs (HRTF) is available from MIT-Medialab A proper routine has been developed for interpolating the required IR starting from the knowledge of the direction of arrival of each discrete early reflection.

Data-base of HRTF impulse responses The complete set of binaural IRs measured on the Kemar dummy head at MIT-Medialab

Geometry of the HRTF data-base Number of measurements at each elevation

Interpolation of the three nearest HRTFs

Evaluation of the weights the weight Pi (i = 1,2,3) relative to each HRTF is obtained calculating the opposite triangle area and dividing it for the total initial triangle area; so we have P1+P2+P3 =1.

Computation of the binaural IR At the exact arrival time of the received ray, an averaged binaural IR is added to the global impulse response. The averaged IR is obtained by a frequency domain interpolation between the three HRTF complex spectra: The interpolation is actually done in the frequency domain, on the magnitude and unwrapped phase of the three HRTFs The octave-band amplitude equalization corresponding to the room transfer function is also applied in the frequency domain FFT and IFFT are used for converting between time domain and frequency domain

The Stereo Dipole The cross-talk cancellation allows for the replica of the recorded signals at the ears of the listener

Design of cross-talk canceling filters First, a binaural measurement is made in front of the Stereo Dipole loudspeakers

Theory of cross-talk canceling filters The regularization parameter, e, has to be adjusted by trials

Example Measured impulse responses h

Example Computed long-FIR inverse filters f

The Dual Stereo Dipole It is a four-channel system, in which a frontal stereo dipole is employed for reproducing the sound coming from directions located in the frontal hemispace, and the rear stereo dipole reproduces the sound coming from the rear hemispace Usually the rear loudspeaker pair requires a larger angle than the frontal one

The Ambiophonics method The system is based on two indipendently designed groups of loudspeakers: a Stereo Dipole, responsible for the reproduction only of the direct sound and early reflections coming from the stage, a surround periphonic array, driven by real-time convolution with room impulse responses (it can be quite irregularly shaped)

Synthesis of the IRs for surround convolution For any loudspeaker in the surround array, the WXYZ channels of a B-format IR can be processed, extracting a single (mono) response of a virtual microphone pointing along a given versor r (rx, ry, rz):

The Double-reverberation problem

Conclusions Auralization can be done nowadays not only by the traditional binaural method (headphone listening), but also with modern methods of loudspeaker presentation Ambiophonics revealed to give significant advantages over the two surround systems which constitutes it (1st order Ambisonics and Stereo Dipole). In cases of limitation in number of reproduction channels, a Dual-Stereo-Dipole can also be very effective. When multiple listeners are required in a large listening area, the preferred method is 2nd order Ambisonics. The computational power required by these multichannel reproduction methods can be obtained cheaply by means of a modern PC running one of the available free convolution softwares

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