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.

Research in 3D Sound

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 (a voice, a music instrument, a plane…) and also their tones.
– a spatial dimension, which allows us 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 in terms of 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 (DVD-Audio and Super Audio CD) 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 of 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. In addition, 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 exactly 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”. In order 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 fields processing.

The Fourier-Bessel transform decomposes any acoustic field as a superposition of elementary acoustic fields: the Fourier-Bessel functions. Historically, any actual audio process (synthesizers, filters, effects…) have been based on the signal processing theory which use the properties of the Fourier transform. Now the Fourier-Bessel functions are to the acoustic fields what Fourier functions (complex exponentionals) are to the audio signals. Utilizing Fourier-Bessel functions, Trinnov Audio developed a very powerful theory of acoustic field processing allowing infinite possibilities of manipulation

The Fourier-Bessel transform of an acoustic field is similar to the Fourier transform of a signal. More precisely, the Fourier transform describe 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

champAnimThe acoustic pressure value is defined for each point in space ant 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

coeffAnimThe spectrum gives the contributions (or weights) of each Fourier-Bessel function in the construction 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 mathematical representation is the fundamental tool for pioneers in acoustic field processing.

A directivity function


A directivity function can be associated to the Fourier-Bessel spectrum (spherical Fourier transform).
This is 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.

This is 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 the frequency

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

Variation of the order

varOrderAt constant frequency, both the spatial zone of perfect representation and the accuracy of the directivity increase with the order.

Moving sound source

var-DistAt constant frequency and order, the spatial zone of perfect representation is constant and the directivity pattern represents the position of the source: the main lobe points to the source while the phase represents the distance.