Soundfield Navigation using an Array of Higher-Order Ambisonics Microphones

Transcription

1 Soundfield Navigation using an Array of Higher-Order Ambisonics Microphones AES International Conference on Audio for Virtual and Augmented Reality September 30th, 2016 Joseph G. Tylka (presenter) Edgar Y. Choueiri 3D Audio and Applied Acoustics (3D3A) Laboratory Princeton University 1

2 Soundfield Navigation HOA mic. 4 HOA mic. 3 Sound source HOA microphone Accurate region Listening position HOA mic. 2 Valid region See: [1] Poletti (2005). Three-Dimensional Surround Sound Systems Based on Spherical Harmonics. 2

3 Overview Previous work Proposed method for soundfield navigation Evaluation - numerical simulations and metrics Results Conclusions and future work 3

4 Previous Work Collaborative blind source separation [5] Ideal for soundfields with discrete sources Degradation of sound quality due to artifacts Weighted average of ambisonics signals [6] Comb-filtering and skewed localization [5] Zheng (2013). Soundfield navigation: Separation, compression and transmission. [6] Southern, Wells, and Murphy (2009). Rendering walk-through auralisations using wave-based acoustical models. 4

5 Proposed Method 5

6 Basic Principle Sound source HOA mic. 1 Listening position HOA mic. 2 HOA mic. 3 Valid region 6

7 Ambisonics Translation z ~d b(k) b(k) =T(k; ~ d) a(k) a(k) y x [7] Zotter (2009). Analysis and Synthesis of Sound-Radiation with Spherical Arrays. See: [9] Gumerov and Duraiswami (2005). Fast Multipole Methods for the Helmholtz Equation in Three Dimensions. 7

8 Proposed Method Pose as frequency-dependent inverse problem Write translation matrix from listening position to each of P microphones When multiplied by x, should give measured signals Compute regularized pseudoinverse via singular value decomposition of M M x = y 2 p w1 T( ~ 3 d1 ) p w2 T( d2 ~ ) x = p wp T( ~ dp ) Translation matrices Unknown HOA signals x = V + U y Least-squares estimate 2 p 3 w1 b p 1 w2 b p wp b P Measured HOA signals 8

9 Microphone Validity HOA signals from mic. 1 HOA signals from mic. P Compute HOA signals at listening position Interpolated HOA signals Detect and locate nearfield sources [5] Determine valid mic s Renormalize weights Microphone positions Listening position Interpolation weights [5] Zheng (2013). Soundfield navigation: Separation, compression and transmission. 9

10 Evaluation 10

11 Numerical Simulations " Simulation #1 Simulation #2!"#$Δ " (&) #! Δ ϕ! Δ (%)!"#$Δ! Key Point source HOA microphone Listening position 11

12 Localization Prediction Using precedence-effect based localization model [11] 1. Transform to plane-wave impulse responses (IRs) 2. Split each IR into wavelets 3. Threshold to find onset times 4. FFT to find frequencydependent source gains Plane-wave IR High-pass Find peaks Window Wavelets [11] Stitt, Bertet, and van Walstijn (2016). Extended Energy Vector Prediction of Ambisonically Reproduced Image Direction at Off- Center Listening Positions 12

13 Results 13

14 Recall: Numerical Simulation #1 " #! Δ ϕ! Key Point source HOA microphone Listening position 14

15 Coloration: Simulation #1 Weighted Average Method Proposed Method!Δ!Δ $"" "%! #! #"!" #"" $"" "%! #! #"!" #"" (! (! #!" '# #!" '#!"#$%&'() ((*) #""!" &! %# $! "#!"#$%&'() ((*) #""!" &! %# $! "# " ϕ =! ϕ =! " Distance: rs = 1 m Input order: Lin = 4 Spacing: Δ = 0.5 m!" #""!"" #"""!""" #"!!"#$%#&'( ()*)!" #""!"" #"""!""" #"!!"#$%#&'( ()*) 15

16 Coloration: Simulation #1 continued!!" = %!Δ "$! #! #"!" #""!"#$%&'() ((*) #""!" "!!" = $!!" = #!!" = "!!" =!!" #""!"" #"""!""" #"!!"#$%#&'( ()*) Proposed method only Distance: rs = 1 m Azimuth: ϕ = 45 Spacing: Δ = 0.5 m Result: the proposed method achieves negligible coloration for kδ 2Lin 16

17 Localization: Simulation #1!Δ +! % ' ( ) ## #% #' #(!"#$%&'$(&") *++"+ ϵ ( ) *! &! $! 7.7!"#$%&"' ()$* +"$-,-! 3.9!"#!"$!"%!"&!"'!"(!") #!""#$ %&#'()* Δ (+) Result: for small spacings (Δ < 0.5 m), the proposed method ( Reg-LS ) achieves improved localization Distance: rs = 1 m Input order: Lin = 4 Frequency: f = 1 khz Averaged over azimuth 17

18 Localization: Simulation #1 continued Δ ϵ ( ) = Weighted Avg. Δ ( ) Proposed method only Distance: rs = 1 m Frequency: f = 1 khz Averaged over azimuth Result: the proposed method achieves accurate localization for kδ 2Lin 18

19 Recall: Numerical Simulation #2!"#$Δ " (&) Δ (%)!!"#$Δ Key Point source HOA microphone Listening position 19

20 Localization: Simulation #2 Δ Δ ϵ ( ) ϵ ( ) Δ ( ) Δ ( ) (a) Source position rs = (0.75Δ, 0, 0) (b) Source position rs = (0.75Δ, 0.75Δ, 0) Proposed method only Input order: Lin = 4 Frequency: f = 1 khz Averaged over azimuth Result: inclusion of invalid microphones can significantly degrade localization 20

21 Summary and Conclusions Presented a method of soundfield navigation: Regularized, least-squares using an array of HOA microphones Explored coloration and localization errors For a pair of microphones: kδ 2L in Demonstrated error introduced by invalid microphones Future work: Validate objective predictions Minimize spectral coloration 21

22 References [1] M. A. Poletti, Three-Dimensional Surround Sound Systems Based on Spherical Harmonics, J. Audio Eng. Soc., vol. 53, no. 11, pp (2005). [2] N. Hahn and S. Spors, Physical Properties of Modal Beamforming in the Context of Data-Based Sound Reproduction, presented at the 139th Convention of the Audio Engineering Society, (2015 Oct.) convention paper [3] F. Winter, F. Schultz, and S. Spors, Localization Properties of Data-based Binaural Synthesis including Translatory Head-Movements, presented at the 7th Forum Acusticum, (2014 Sept.). [4] J. G. Tylka and E. Y. Choueiri, Comparison of Techniques for Binaural Navigation of Higher-Order Ambisonic Soundfields, presented at the 139th Convention of the Audio Engineering Society, (2015 Oct.) convention paper [5] X. Zheng, Soundfield navigation: Separation, compression and transmission, Ph.D. thesis, University of Wollongong (2013). [6] A. Southern, J. Wells, and D. Murphy, Rendering walk-through auralisations using wave-based acoustical models, presented at the 17th European Signal Processing Conference (2009). [7] F. Zotter, Analysis and Synthesis of Sound-Radiation with Spherical Arrays, Ph.D. thesis, University of Music and Performing Arts Graz (2009). [8] C. Nachbar, F. Zotter, E. Deleflie, and A. Sontacchi, ambix - A Suggested Ambisonics Format, presented at the 3rd Ambisonics Symposium (2011 June). [9] N. A. Gumerov and R. Duraiswami, Fast Multipole Methods for the Helmholtz Equation in Three Dimensions, Elsevier Science (2005). [10] M. A. Gerzon, General Metatheory of Auditory Localisation, presented at the 92nd Convention of the Audio Engineering Society, (1992) convention paper [11] P. Stitt, S. Bertet, and M. van Walstijn, Extended Energy Vector Prediction of Ambisonically Reproduced Image Direction at Off-Center Listening Positions, J. Audio Eng. Soc., vol. 64, no. 5, pp (2016). [12] J. Fliege and U. Maier, The distribution of points on the sphere and corresponding cubature forumlae, IMA Journal of Numerical Analysis, vol. 19, no. 2, pp (1999). 22