the generation of panning laws for irregular speaker arrays using heuristic methods

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A presentation made at the 31st International AES conference in 2007 on the generation of higher order Ambisonic decoders for the irregular, 5 speaker, ITU speaker arrangement.

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the generation of panning laws for irregular speaker arrays using heuristic methods

  1. 1. THE GENERATION OF PANNING LAWS FOR IRREGULAR SPEAKER ARRAYS USING HEURISTIC METHODS. Dr Bruce Wiggins Signal Processing Applications Research Group University of Derby
  2. 2. Introduction <ul><li>In 2003, Craven proposed a new panning algorithm for the ITU-R BS.775-1 standard speaker arrangement. </li></ul><ul><li>This panning law used 0 th to 4 th order circular harmonics and was based upon the Ambisonic decoder principles suggested by Gerzon. </li></ul><ul><li>Although Craven’s derivation method was not discussed, the heuristic methods shown by Wiggins (2003, 2004) can be used. </li></ul>
  3. 3. Ambisonics - Overview <ul><li>Ambisonics represents a set of rules used for the design of a decoder/reproduction system. </li></ul><ul><li>It uses (in its simplest form) a velocity and energy vector analysis of the system to quantify (and optimise) its performance. </li></ul><ul><li>An Ambisonic system is one where: </li></ul><ul><ul><li>The decoded velocity and energy vector angles agree and are substantially unchanged with frequency. </li></ul></ul><ul><ul><li>At low frequencies (below around 400 Hz) the low frequency velocity vector magnitude is equal to 1 for all reproduced azimuths. </li></ul></ul><ul><ul><li>At mid/high frequencies (between around 700 Hz and 4 kHz) the energy vector magnitude is substantially maximised across as large a part of the 360 0 sound stage as possible. </li></ul></ul>
  4. 4. Frequency Band Choices <ul><li>Bamford (1995) showed that 1 st order Ambisonics is essentially a volume solution up to around 380Hz. </li></ul><ul><ul><li>The velocity vector analysis essentially optimises for this situation. </li></ul></ul><ul><ul><li>This is a measure of the resultant direction of the sound wave at the central point. </li></ul></ul><ul><li>Above this frequency, the energy vector analysis is used to make sure the energy is predominately coming from the correct direction. </li></ul>
  5. 5. Decoders for Regular Speaker Arrays <ul><li>1 st order Example – using a mixture of a 0 th (omni) and 1 st (figure of 8) mic, any 1 st order mic pattern can be created. </li></ul><ul><li>1 st order Example – using a mixture of a 0 th (omni) and 1 st (figure of 8) mic, any 1 st order mic pattern can be created. </li></ul>
  6. 6. 1 st Order Decoders
  7. 7. Decoders for irregular speaker arrays <ul><li>Irregular decoders cannot be optimised so easily. </li></ul><ul><li>For left/right symmetrical systems: </li></ul><ul><ul><li>Amplitude </li></ul></ul><ul><ul><li>Polar pattern </li></ul></ul><ul><ul><li>Angular spread </li></ul></ul><ul><li>Must all be optimised, per speaker pair. </li></ul><ul><li>This means solving a set of non-linear simultaneous equations. </li></ul><ul><li>Heuristic methods can be used to solve this problem. </li></ul>
  8. 8. Higher Order Irregular Decoders <ul><li>Same problem as 1 st order, just more variables. </li></ul><ul><li>Higher order comonents are used to ‘steer’ the polar patterns into: </li></ul><ul><ul><li>More directional responses at the front </li></ul></ul><ul><ul><li>Irregular shapes for the rear </li></ul></ul>
  9. 9. Tabu Search Algorithm <ul><li>Each pair of speakers has 9 adjustable parameters. </li></ul><ul><li>Centre speaker has 5. </li></ul><ul><li>23 parameters are available in total for a 5 speaker ITU decode. </li></ul><ul><li>Decoders ‘fitness’ is using combination of 6 measures: </li></ul><ul><ul><li>Pressure </li></ul></ul><ul><ul><li>Velocity Magnitude </li></ul></ul><ul><ul><li>Velocity Angle </li></ul></ul><ul><ul><li>Energy </li></ul></ul><ul><ul><li>Energy Magnitude </li></ul></ul><ul><ul><li>Energy Angle </li></ul></ul>
  10. 10. Fitness Equation Weightings <ul><li>The fitness measures are combined depending of the type of decoder needed: </li></ul><ul><li>Low frequency decode: </li></ul><ul><ul><li>Optimise – Pressure, Velocity Magnitude, Velocity Angle, Energy Angle </li></ul></ul><ul><li>High frequency decode: </li></ul><ul><ul><li>Optimise – Energy, Energy Magnitude, Energy Angle, Velocity Angle. </li></ul></ul><ul><li>Frequency independent decode: </li></ul><ul><ul><li>Same as High frequency, but try to improve velocity magnitude as well. </li></ul></ul>
  11. 11. Example 2 nd Order Decoders <ul><li>Here the weightings of the fitness functions were adjusted as per the last slide. </li></ul>Frequency Independent High Frequency Low Frequency
  12. 12. Tabu Search Application
  13. 13. Further Analysis of Optimised Decoders <ul><li>Irregular decoders have more than one solution as they are always a compromise. </li></ul><ul><li>Further analysis can be carried out using HRTF data. </li></ul><ul><li>It has been previously shown that similar decoders (according to energy/velocity vector analysis) can have different results using HRTF analysis (Wiggins 2003, 2004). </li></ul><ul><li>A simulation of ‘head turning’ tends to give the largest observable difference between decodes. </li></ul><ul><li>These techniques will be applied to three 4 th order and one 1 st order decoder. </li></ul>
  14. 14. 4 th Order Decoders Craven Decode Max Me Mv 1 Max Me Mv 2 Max Ae Av 0.70 0.50 0.10 0.25 0.15 0.00 Max Ae Av 0.60 0.90 0.10 0.15 0.15 0.00 Max Me Mv 2 0.60 0.50 0.10 0.15 0.25 0.00 Max Me Mv 1 AeFit MeFit EFit AvFit MvFit PFit Decoder type
  15. 15. HRTF Analysis – Forward Facing Craven Decode Max Me Mv 1 Max Me Mv 2 Max Ae Av
  16. 16. Facing 45 0 From Front Craven Decode Max Me Mv 1 Max Me Mv 2 Max Ae Av
  17. 17. References <ul><li>Wiggins, B. et al. (2003) The Design and Optimisation of Surround Sound Decoders Using Heuristic Methods. Proceedings of UKSim 2003, Conference of the UK Simulation Society p.106-114 . </li></ul><ul><li>Wiggins, B. (2004), An Investigation into the Real-time Manipulation and Control of Three-dimensional Sound Fields, PhD thesis, University of Derby, Derby, UK. </li></ul><ul><li>Craven, P. (2003), Continuous Surround Panning for 5-speaker Reproduction, AES 24th International Conference , Banff, Canada. </li></ul><ul><li>Bamford, J.S. (1995) An Analysis of Ambisonic Sound Systems of First and Second Order , Master of Science thesis, University of Waterloo, Ontario, Canada. </li></ul>

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