# Background To The Application¶

## Acoustical Model¶

The efficient calculation of accurate and useful response curves in strongly varying environments (e.g. quasi-freefield outdoor arenas large indoor arenas or smaller values) is a task that has been challenging the industry for years and is still being actively researched.

CODA makes use of an algorithm or calculation model that has emerged as standard over the years and is widely accepted within the industry,
which we call *Hybrid Summation* or *Direct Sound Hybrid Summation*.
This model is based on the Precedence effect or law of the first wavefront and thus **does not take any reflections into account**.
The proper calculation of reflections requires more sophisticated and time-consuming techniques like Ray Tracing or (FM)BEM ((Fast Multipole) Boundary Element Methods).
Especially physically-correct techniques like the Boundary Element Method require special treatment in order to be usable for such scenarios, as they usually assume
a closed geometry, but only infinitely thin bodies (surfaces) are available.
In addition to this, the mentioned techniques would require the entry of material properties like absorption factory to give useful results.
All of the above points make the more sophisticated techniques unsuitable for this purpose, at least for now.

This also means that other acoustical effects like inter-cabinet coupling of (closely) stacked low frequency transducers leading to an increase in radiation impedance and a change of response or shadowing / diffraction from other cabinets (e.g. when stacking subwoofers or flying low frequency extensions behind a Line Array are not taken into account.

There are more acoustical effects (like the influence of wind), but in order to take those into account, one must solve similar challenges as for the other previously mentioned effects.

So, like the name *Direct Sound Hybrid Summation* says, only the Direct Sound radiated by the placed speakers is taked into account.

However, the method to actually obtain a response from the placed speakers, the exact summation method, is still unexplained.
This is where the **Hybrid Summation** part comes in.

The Hybrid Summation is a two-level summation. First, speakers placed within a single instance (hang, stack) are summed together using complex summation.
Complex summation is also sometimes termed *coherent summation* and takes phase differences into account. Complex summation is the physically correct way
for summation of sound sources and gives highly accurate results across the entire frequency range including spurious directivity effects from Line Arrays.
Complex summation gives the widely known, approximately 6dB more (actually around 5.9dB) level when two identical sources are combined.

After the instance responses have been obtained, the actual hybrid summation stage follows. The hybrd summation stage makes use of both complex (coherent) and energetic (incoherent) summation and a mix of both. Energetic summation assumes random phase and thus gives +3dB level when combining two identical sources.

In the low frequency range, the instance levels are combined using complex summation which ensures that directivity patterns in the low frequency range are accurately calculated. Starting at the 200Hz frequency range, the hybrid summation slowly shifts (over a bandwidth of one octave) from complex summation to energetic summation, until a fully energetic summation is employed starting at the 400Hz range.

Energetic summation in the MF / HF frequency range has been proven useful many times in a huge variety of different real world scenarios. It has the distinct advantage that unhelpful, fine-grained interference patterns are suppressed.

Surfaces marked as Obstacles are taken into account using geometric intersection tests and block the entire frequency range of the respective balloon. They do not add any reflections.

## Technical Specifications of the Acoustic Subsystem¶

CODA believes that customers should be able accurately assess the quality of the software they use as a basis of their daily work and thus has decided to publish technical specifications of the acoustic subsystem of the System Optimiser software.

**General**

The internal frequency resolution of System Optimiser is 1/24th Octave (standard rounded center frequency), which provides by far enough accuracy for the purpose of the software. In total, 246 frequencies are used and calculated.

**Atmospheric Model**

CODA makes use of a sophisticated and highly accurate model for calculation of frequency-dependent atmospheric absorption coefficients that has been independently published and peer-reviewed 1 2 3

**Balloons**

Balloons are the heart of System Optimiser and CODA has put a significant amount of time and effort into the development of the balloons.

Balloons in System Optimiser are fully complex which means they contain amplitude and phase data. Balloons in System Optimiser range from 2° spatial resolution (Line Arrays) to 10° spatial resolution (subwoofers). Please note that currently some speakers are still being modelled als truly omnidirectional, but will be improved in due time. Interpolation between data points is done using a combination of sophisticated techniques including Spherical Harmonics / Acoustic Multipoles for increased accuracy. Please note that this technology increases the actual resolution over the data resolution of the balloon.

The creation of balloons from acoustical measurements is a complex process with many steps that involves a considerable number of proprietary techniques developed by and for CODA, e.g. optimised Spherical / Spatial Continuous Phase unwrapping and special resampling algorithms.

Balloons contain data on the 1/24th Octave spaced frequency grid used throughout System Optimiser (and thus can contain a maximum of 246 frequencies with thousand of data points each). Balloons make use of symmetry where appropriate. Data is stored using 32-bit floating point numbers and optimised normalisation.

**Spatial Sampling**

Polygons and Quads are currently sampled on a cartesian grid with 30cm distance between rows and columns. Sectors are sampled with 3° angular resolution and 30cm radial / slant resolution.

Please note that this is subject to change and users will be able to adjust the resolution to their own needs soon.

Interpolation between sampling points for rendering purposes is done using standard bilinear interpolation.

Please note that Microphones placed on surfaces do **not** perform interpolation between adjacent data points, but instead calculate an entirely new response.

## List of included balloons¶

Please refer to the List of Available Loudspeakers and Presets

Footnotes

- 1
Bass, H. E., Sutherland, L. C., Piercy, J., and Evans, L., “Absorption of sound by the atmosphere”, in

*IN: Physical acoustics: Principles and methods. Volume 17 (A85-28596 12-71). Orlando*, 1984, vol. 17, pp. 145–232.- 2
Bass, L. C. Sutherland, and A. J. Zuckerwar, “Atmospheric absorption of sound: Update,”

*The Journal of the Acoustical Society of America*, vol. 88, no. 4, pp. 2019–2021, 1990.

- 3
Bass, L. C. Sutherland, A. J. Zuckerwar, D. T. Blackstock, and D. M. Hester, “Atmospheric absorption of sound: Further developments,”

*The Journal of the Acoustical Society of America*, vol. 97, no. 1, pp. 680–683, 1995.