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Robust 2D Surround Sound Reproduction for nonuniform loudspeaker layouts Mark Poletti Industrial Research Ltd

Robust 2D Surround Sound Reproduction for nonuniform loudspeaker layouts Mark Poletti Industrial Research Ltd. Introduction. Basic idea of surround sound Panning functions and interpolants Robustness analysis Transducer variability High frequency interference Optimum panning functions

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Robust 2D Surround Sound Reproduction for nonuniform loudspeaker layouts Mark Poletti Industrial Research Ltd

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  1. Robust 2D Surround Sound Reproduction for nonuniform loudspeaker layoutsMark PolettiIndustrial Research Ltd

  2. Introduction • Basic idea of surround sound • Panning functions and interpolants • Robustness analysis • Transducer variability • High frequency interference • Optimum panning functions • Least squares panning functions • Area of sound field reproduction • Directional penalty function • ITU layout design • Comparison with Craven, pairwise panning

  3. Record the directional characteristics of a sound field Reproduce the sound field using an array of loudspeakers L loudspeaker means we need L ‘microphones’ - each looking in the direction of an associated speaker Or – we can synthesis the L microphone responses from a trigonometric decomposition of the (azimuthal) soundfield Microphone responses for a single sound source are “panning functions” Basic Idea

  4. Derivation of panning functions • Pressure matching • L speakers, with speaker amplitudes (‘weights’) wl • Mode matching Both of these are Interpolation problems Interpolants from sampling theory apply

  5. Uniform case: L Odd • Produces odd circular interpolants (circular sinc) for uniform periodic sampling L=5

  6. Uniform case: L Even • Produces even circular interpolants for uniform periodic sampling L=6

  7. Soundfield reproduction accuracy • Over what frequency range or area (kR) is reproduction accurate? • Simple analysis: If speakers are closer than wavelength/2 reconstruction is accurate More accurately: eg f=1 kHz, R=100mm, N=5

  8. Surround Sound - Reproduction Error N=kd=2kr More exactly: N=2kr+1

  9. Interpolants for nonuniform sampling? • Eldar & Margolis derived real interpolants • Proc IEEE Conf El. Cct, Sys., 2004 L odd L even These equal asinc functions for uniform samples

  10. Interpolants for ITU BS-775-1 • Interpolants for samples at 0, ±30, ±110 degrees Rms sum Interpolants become large for very irregular layouts What are the effects of these large values?

  11. Robust panning functions • Assume errors in loudspeaker magnitudes and phases • Consider interference at high frequencies (r>0) • In both cases, errors are proportional to the sum of squared weight magnitudes u is complex normal Variance s2 governs magnitude and phase error 1

  12. Robust panning functions • Panning functions should have weight powers that sum to one • Sound pressure reconstruction also means weights sum to one • This is termed double complementarity • Only approximately met with real functions Double complementarity requires phase quadrature for L=2. Complex for L>2

  13. Least squares design of robust panning functions • We require: • Write this out for N positions (rn,Фn), n=1:N w found by solving matrix equation at each source angle

  14. Directional penalty • Standard least squares solution does not localise panning functions to individual speakers • We use a directional penalty function Minimise error with penalty function Penalty function is 0 for nearest speaker & is large for speakers far away from desired direction Least squares solution: B=diag(b)

  15. ITU panning functions: example Least squares 4th order design Craven’s velocity vector energy vector 4th order solution

  16. Radial error Craven Interpolant Least squares

  17. Radial error with perturbation Interpolant Weights wl(1+u) Monte Carlo simulation Average of 10 results 10 degrees rms error Least squares

  18. Velocity direction at origin Craven Least squares

  19. U velocity- least squares 50 degrees

  20. U velocity-Craven 50 degrees

  21. Pairwise panning-comparison • Uniform 5-speaker array (offset) Least squares, β=8 Optimum stereo matching of pressure at low frequencies

  22. Average radial error • Averaged error over angle at each radius Interpolant Lsq Pairwise kr=3.2 r=87.5mm f=2 kHz

  23. Average radial error • 10 iterations with 10 degree rms error

  24. Velocity direction Pairwise Lsq

  25. Conclusions • Standard interpolants are non robust for nonregular loudspeaker layouts (nonuniform layouts are less robust) • Robust (real) panning functions approximate a double complementarity property • Least squares design with directional penalty can produce robust panning functions • Robust solution can be varied to trade off low frequency accuracy versus high frequency interference control

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