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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.

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

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