How does Acoustic Correction work?

The Optimizer starts with the acoustic phenomenon that are mostly deterministic, and gradually moves to the ones that are mostly statistic. This automated room correction combines both IIR filters and FIR filters. The IIR filters allow for very accurate equalization in the low range, while the FIR filters work full range.

• Correction of Early Reflections (Direct Field):
  The Optimizer analyses the measurements in the time-frequency domain to identify Early Reflections. Depending on their amplitude, frequency, direction and arrival time, the Optimizer will compensate for them to a certain extent, or not try to compensate for them. After this process, each loudspeaker's response is "clean" from the early reflections that it is possible to correct with digital technology. The other reflections are not touched.

• Correction of the Room Energy:
  In this second stage the Optimizer analyzes the measurements in the frequency domain only (the response of the system in steady state). 
• Compensation of Resonance Modes (in the low range):
  the Optimizer identifies resonance modes in the range where they can be clearly differentiated, roughly up to 300Hz. It applies individual filters to compensate each resonance mode.
• Smoothing of the reverberation (in the mid and high range):
  The Optimizer analyzes the room's frequency response, related to the coloration of the room's reverberation. Another filter is applied to smoothly compensate for this coloration.

All the subtlety of the Optimizer resides in its knowledge of the defects that shouldn't be tried to correct for without creating even more problems.

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How does Loudspeaker Positions Remapping work?

The Remapping technology of the Optimizer is based on the ability to calculate the acoustic field that is produced by a set of loudspeakers. This calculation is possible thanks to the Fourier-Bessel decomposition of the acoustic field into a certain number of coefficients that correspond to the spherical harmonics. Just as the Fourier decomposition is commonly used to analyze a signal in the frequency domain, the Fourier-Bessel decomposition can be used to analyze an acoustic field in the space domain, by decomposing into a sum of elementary radiation patterns that are referred to as spherical harmonics in mathematics.

The function that provides the resulting acoustic field from the input signals is called a "radiation matrix". In a pseudo math notation: Input Signal * Radiation Matrix = Acoustic Field

a) Real radiation matrix:
the Optimizer first computes the radiation matrix of the real system, in other words the radiation matrix that corresponds to the measured loudspeaker positions. This is possible because the Optimizer knows the exact positions of the loudspeakers in 3D. 

This radiation matrix for the real system allows to calculate the actual acoustic field that is produced by the measured loudspeaker placement. 

b) Ideal radiation matrix:
on the other hand, the Optimizer can calculate the radiation matrix for the reference placement, because the loudspeaker positions of the reference placement are, by definition, clearly defined. 

This radiation matrix for the reference system allows to calculate the ideal acoustic field that would be produced if the loudspeakers were positioned correctly, according to the reference placement. 

c) Remapping matrix:
the last stage is to find out the additional processing that should be applied to the input signal in order to obtain the ideal acoustic field from the measured loudspeaker system. This is done by inverting the Real Radiation Matrix:

Remapping Matrix = Radiation Matrix of the ideal system * (radiation matrix of the real system)-1

Conclusion:
This Remapping Matrix is computed once (after the loudspeaker positions have been measured) and applied in real time to the input signals to compute the output signals that should be sent to each loudspeaker in order to obtain the reference acoustic field. 

Note: in the case where the number of inputs is different from the number of outputs, one could describe this remapping technology as a universal downmixing/upmixing algorithm for 3D audio reproduction. 

See Trinnov's AES Convention Paper 6375 for a detailed explanation of louspeaker remapping.

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3D Simulations

As illustrated in the following 3D simulations, deconvolution provides spectacular results when applied to the compensation of early reflections.

When a loudspeaker produces a wave front in a room, the walls produce secondary wave front. At the begining is is easy to identify each elementary reflections but after some time, the reflections are so numerous that it becomes impossible to separate them, it is the reverberation.

The Optimizer compensates separately and with different methods the early reflections and the reverberation. Deconvolution provides best results when only applied to early reflections, while minimal phase (or linear phase) equalization provides best results when applied to the reverberation.

When a loudspeaker is placed in free air or in anechoic chamber, only one wave front is produced at the listening spot. Let's consider the first reflection produced by a wall placed immediatly behind the loudspeaker. The reflection against the wall creates a secondary wave front. When the loudspeaker is producing a single pulse, 2 wave fronts are produced at the listening spot. When this condition is compensated with deconvolution techniques, the second wave front is strongly cancelled at the listening position, where any other equalization method would fail. The result of deconvolution leads the loudspeaker to fire a second time after producing the primary pulse and to produce a second pulse whose wave front is the identical inverse to the wave front of the reflection. The inversed wave front produced by the loudspeaker cancels the reflection and the original single wave front is retrieved.

		Propagation of a wave in a room of 5m x 4m reflexion.wmv (16.3 MB)
		Before deconvolution: wave front produced by a loudspeaker in free air conditions hp.wmv (2.9 MB)
		Before deconvolution: secondary wave front introduced by a reflection hpfirstref.wmv (3.5 MB)
		After deconvolution: modified wave front produced by the loudspeaker in free air conditions hpandcorrec.wmv (3.1 MB)
		After deconvolution: reflection cancelled allCorrec.wmv (3.5 MB)