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RESEARCH IN 3D SOUND

Trinnov Audio allocates extensive research efforts to contribute to the improvement of audio quality. We focus on one of the greatest scientific challenges: spatial audio. Our scientific papers are considered as world-class contributions by many renowned experts and have been relayed in the prestigious JAES (Journal of the Audio Engineer Society).

The result of this continuous R&D effort is a leading position in the emerging scientific area of DIGITAL ACOUSTICS – the processing of acoustic fields in 3D. Acoustic field processing is to spatial audio what signal processing is to discrete signals. It provides understanding and control of spatial audio to bring the performances to the next level.

The future of audio lies in the control of the spatial dimension of sound.

Any sound event presents two aspects

– a TIME dimension, which allows us to recognize the different sounds (voice, music instrument, plane…) and also their tones.

– a SPATIAL dimension, which makes it possible to localize each sound (the voice is ahead, the plane is high…) and also recognize the place where they are located (a church, a street…).

The continuous progress regarding computing power and storage capacity offers new perspectives in the field of audio.

However, ANY FURTHER IMPROVEMENT OF THE TEMPORAL ASPECT IS ALMOST USELESS for the major part of the listeners. For example, the new high-resolution formats have today reached the limits of the human’s hearing capacities. On the contrary, the spatial performances of today technologies remain limited.

Unfortunately, the developments dedicated to spatial audio aspect are limited by the deficiency in the theoretical foundation of solids, which is the direct opposite to the temporal aspect which is based on the signal theory (signal processing). Consequently, the need for new research to control sound as a whole is emerging.

Any sound event creates wave phenomenon expending in time and in the three space dimensions called ACOUSTIC FIELD.

For a better understanding of the power of this model, let’s suppose that one could perfectly capture an acoustic field, for example, the one produced by an orchestra in a concert hall. Also, let’s suppose that one could reproduce the identical acoustical field in a listening room.

In this case, the audience in the listening room should hear the same reality than the audience in the concert hall, from both a temporal point of view (as the today’s techniques make it possible) and a spatial point of view.

While High-Fidelity focused on the accurate reproduction of audio signals, the accurate reproduction of the whole acoustic field opens the way to “High Spatial Fidelity” or “High Spatial Resolution.” To fully take advantage of this more exact representation, Trinnov Audio engaged an extensive research program to provide cutting-edge solutions to these new challenges.

Fundamental acoustics offers a powerful theoretical tool which allows us to describe the acoustic fields: 

THE FOURIER-BESSEL TRANSFORM.

Very specialized and poorly documented, it has remained until now unexploited in audio. Trinnov Audio based his research work on this theoretical tool as well as other sciences, including mathematics and signal processing. As a result, Trinnov Audio has developed.

A NEW THEORY FOR ACOUSTIC FIELD PROCESSING

The Fourier-Bessel transform decomposes any acoustic field as a APPLICATIONS

The power of today’s signal processing comes from the manipulation of the Fourier functions (exponential or sine/cosine). Similarly, the power of 3D ACOUSTIC FIELD PROCESSING is based on the manipulation of FOURIER-BESSEL functions. This new theory has led us to develop new technologies allowing to record, manipulate, and reproduce acoustic fields.

Trinnov’s technologies for 3D sound provide new solutions to the real world challenges of sound engineers, acousticians, and sound systems designers.

Spatial recording can be used to make high quality 5.1 recordings. This technology is used in our solution for surround recording, the SRP (Surround Recording Platform).

Spatial playback helps to optimize loudspeaker placement in a room. It is used in our flagship 3D Loudspeaker Remapping technology.

SPATIAL RECORDING OF ACOUSTIC FIELDS

Current technologies of surround recording consider separately the signals provided by each microphone used. Thanks to a radically innovating processing of these signals, the SPATIAL PICK-UP technology makes it possible to optimally exploit all the available microphones to transcribe all the collected information concerning a sound event. It is sufficient to know the spatial characteristics and position of each microphone in the sound space.

Thus, SPATIAL PICK-UP technology brings an optimal answer to every application in function of the specifics constraints (cost, performance, size, simplicity…). Implementation of this technology led us to three prototypes of high spatial resolution microphone using, respectively, 5, 8 and 24 classic microphones. Fourier-Bessel functions allow one to record acoustic fields using any number of the capsule of any type with any array organization (any position, any orientation). More detailed information is available in our scientific paper presented at the 114th AES convention in Amsterdam,
A New Comprehensive Approach to Surround Sound Recording

The standard signal processing theory provides a strong scientific basis for time sampling: a signal can be sampled in time without losses. Similarly, Trinnov Audio developed a generalized theoretical frame for spatial sampling. As a result, an acoustic field can be analyzed by any arrangement of any acoustic sensor organized at any position and orientation in space. The principle of generalized acoustic field sampling comes as follows:

If the acoustic field that stimulates the sensors is known, it’s possible to determine the signals delivered by these sensors with a linear relation. This linear relation is expressed by a matrix called spatial sampling matrix Which provides the sensors signals from the Fourier-Bessel’s coefficients of the acoustic field they have been exposed to. Now, the microphone principle is precisely the opposite: we know the signals provided by the sensors, and we want to estimate the initial acoustic field. As a result, an acoustic field capture is performed by inverting the spatial sampling matrix using generalized inversion techniques.

SPATIAL PLAYBACK OF ACOUSTIC FIELDS

Today’s “multichannel” technologies consist of providing signals each dedicated to feeding a single speaker so that the listener placed in the middle hear the desired effect. SPATIAL REPLAY technology gathers information describing an acoustic field and applies proprietary processing to determine the signals required for each speaker to reproduce the acoustic field optimally.

Thus, SPATIAL REPLAY technology gives an optimal answer to every application as a function of the specific constraints such as cost, performance, size, simplicity… The application of this technology has permitted Trinnov Audio to develop a prototype using from 2 to 16 speakers with a random arrangement. As there is no restriction to control tens or hundreds of loudspeakers optimally, it gives a strong basis for the future of audio technologies

An acoustic field reproduction system is composed of a set of loudspeaker arbitrary arranged to surround the listening area. The scientific challenge consists in determining the loudspeaker feeds to optimally reproduce a given acoustic field represented by a set of Fourier-Bessel coefficients. The principle of acoustic field reproduction comes as follows:

If the loudspeaker feeds are known, it is possible to determine the acoustic field resulting from the contribution of all the loudspeaker with a linear relation. This linear relation is expressed by a matrix called ‘loudspeaker radiation matrix’ which provides the Fourier-Bessel coefficients of the acoustic field from the signals feeding the loudspeakers. Acoustic field reproduction problem is exactly the opposite: the acoustic field to reproduce is known while the loudspeaker feeds must be determined. As a result, an acoustic field reproduction is performed by inverting the loudspeaker radiation matrix using generalized inversion techniques.

SPATIAL MORPHING OF ACOUSTIC FIELDS

The possibility to accurately reproduce the acoustic field is not enough. Since music production is a creative process, there is a strong demand for specific tools to manipulate the sound environment. Trinnov Audio developed a technology that directly processes the acoustic field: Spatial Morphing. This technology opens to spatial audio the same transformation possibilities than the most advanced photo-editing software offers to picture. As an example, in a full orchestra, a particular musician may be selected and attenuated or amplified, moved around, stretched or diffused in space.

Thus, SPATIAL MORPHING technology brings an innovative solution for a variety of sound design needs. Trinnov Audio has developed prototype software to rotate the sound image, distort or emphasize the soundstage in a particular direction.

According to today’s signal processing technologies, it is often more efficient to manipulate the frequency representation of a signal rather than to manipulate its temporal waveform. As their frequency response traditionally defines an example of filters. The same concept applies to acoustic fields where it is more efficient to manipulate the Fourier-Bessel coefficients representation rather than its spatiotemporal waveform.

Any transformation of a linear acoustic field can be expressed as specific recombination of its Fourier-Bessel coefficients. As a result, the Fourier-Bessel coefficients of the processed acoustic field are obtained by applying a transformation matrix to the Fourier-Bessel coefficients of the unprocessed acoustic field. This generic formulation of acoustic field processing opens infinite possibilities of manipulations. Different transformation categories can be defined as an example:

Spatial rotations: Rotate the entire acoustic field according to the standard three freedom degree of 3D rotations.

Spatial distortions: Applies spatial transformation in the acoustic field; for instance, the sound sources are moved according to an angular distortion law.

Spatial convolution: Adjust the level of details in the acoustic field. As an example can blur a focused recording or, to a certain extent, improve focuses a fussy recording.

Spatial gating makes it possible to select in space part of the entire acoustic field.

The concept of the transformation matrix is the core concept of acoustic field processing. In general, the matrix coefficients for high-resolution acoustic fields (order > 1) are obtained with extremely complex mathematical relations. It has been one considerable challenge for Trinnov Audio to establish and validate these relations. Now, Very complex acoustic field processing can be built by cumulating different type of elementary transformations.

Historically, any actual audio process (synthesizers, filters, effects…) have been based on the signal processing theory which uses the properties of the Fourier transform. Now the Fourier-Bessel functions are to the acoustic fields what Fourier functions (complex exponentials) are to the audio signals.

Utilizing Fourier-Bessel functions, Trinnov Audio developed a very powerful theory of acoustic field processing allowing infinite possibilities of manipulations

The Fourier-Bessel transform of an acoustic field is similar to the Fourier transform of a signal. More precisely, the Fourier transform describes perfectly a signal as a superposition of sinusoids at different frequencies (spectral representation of the signal). In the same way, the Fourier-Bessel transform describes perfectly an acoustic field as a superposition of elementary acoustics fields having different spatial variations (spectral representation of an acoustic field).

Using this theory, it is possible to represent an acoustic field under THREE equivalent points of view:

A PRESSURE FIELD IN SPACE

The acoustic pressure value is defined for each point in space and each instant in time.

This representation directly illustrates waves propagation of the acoustic field, creating a “drops-in-water”-like representation

A FOURIER-BESSEL SPECTRUM

The spectrum gives the contributions (or weights) of each Fourier-Bessel function in the construction of the acoustic field. This representation is extremely powerful as it represents a continuous acoustic field as a set of coefficient changing with time. In other words, it is a digital representation of the acoustic field! Once digitalized, an acoustic field can be controlled by digital processors. Therefore this is a mathematical representation is the fundamental tool for pioneers in acoustic field processing.

A DIRECTIVITY FUNCTION

A directivity function can be associated with the Fourier-Bessel spectrum

(spherical Fourier transform).

This is a very meaningful representation as it gives the apparent direction of the sound.

The color corresponds to the phase of the directivity, connected to the distance of the sources In the standard Fourier theory, the “quickness” of variation of a signal is described by the concept of frequency. The highest the frequency, the fastest the signal varies with time. Similarly, the Fourier-Bessel’s theory describes the “quickness” of variation of an acoustic field by the “spatial frequency,” usually called “order.”

VARIATION OF FREQUENCY

At constant order (or representation precision), the spatial zone of perfect representation decreases with increasing frequency while directivity only varies in phase, not in shape.

FOURRIER-BESSEL

Three-dimensional sound can be described, from a physical point of view, by an acoustic field, which is defined for each point (x,y,z) in space and each instant t using the pressure field p(x,y,z,t). Nevertheless, manipulating an acoustic field using its primary representation p(x,y,z,t) is not easy because it would be necessary to know it for each value of (x,y,z,t). Therefore, an acoustic field is decomposed, in spherical coordinates, into its Fourier-Bessel expansion, offering a much convenient and compact representation.

From the four-dimensional continuous function p(r,0,0,t), the Fourier-Bessel decomposition gives a set of signals called Fourier-Bessel coefficients of the acoustic field, denoted pl,m(t), where l and m are integers that satisfy l = 0 and -l = m = l. In the Fourier-Bessel formalism, l is called the order. In the frequency domain, P(r,0, 0,f) and Pl,m(f) are the Fourier transforms of P(r,0,0,f) and pl,m(t) respectively.

The following expression gives this decomposition:

…where k = 2_f=c and c is the speed of sound, approximately 340 m/s. The Fourier-Bessel expansion is truncated at some order L.

This order determines the resolution of the acoustic field representation. The higher the order, the higher the acoustic field representation fidelity will be, but the more computation power and signals will be required.

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