Soundfield Navigation using an Array of Higher-Order Ambisonics - - PowerPoint PPT Presentation

Soundfield Navigation using an Array of Higher-Order Ambisonics Microphones

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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 www.princeton.edu/3D3A

HOA mic. 2 Valid region

Soundfield Navigation

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HOA microphone HOA mic. 3 Listening position Accurate region HOA mic. 4 Sound source

[1] Poletti (2005). “Three-Dimensional Surround Sound Systems Based on Spherical Harmonics.” See:

Overview

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

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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

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[5] Zheng (2013). Soundfield navigation: Separation, compression and transmission. [6] Southern, Wells, and Murphy (2009). “Rendering walk-through auralisations using wave-based acoustical models.”

Proposed Method

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Valid region

Basic Principle

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HOA mic. 2 HOA mic. 1 Sound source Listening position HOA mic. 3

Ambisonics Translation

y z x ~ d

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b(k) = T(k; ~ d) · a(k) b(k) a(k)

[7] Zotter (2009). Analysis and Synthesis of Sound-Radiation with Spherical Arrays. [9] Gumerov and Duraiswami (2005). Fast Multipole Methods for the Helmholtz Equation in Three Dimensions. See:

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

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M · x = y

˜ x = VΘΣ+U∗ · y      √w1b1 √w2b2 . . . √wP bP           √w1T(− ~ d1) √w2T(− ~ d2) . . . √wP T(− ~ dP )     · x =

Unknown HOA signals Measured HOA signals Translation matrices Least-squares estimate

Microphone Validity

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HOA signals from mic. 1 HOA signals from mic. P Interpolated HOA signals Compute HOA signals at listening position Re- normalize weights Interpolation weights Determine valid mic’s Listening position Detect and locate near- field sources [5] Microphone positions

[5] Zheng (2013). Soundfield navigation: Separation, compression and transmission.

Evaluation

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Numerical Simulations

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! " Δ ϕ #! ! " Δ !"#$Δ !"#$Δ (%) (&)

Simulation #1 Simulation #2 Point source HOA microphone

Key

Listening position

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 frequency- dependent source gains

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Plane-wave IR High-pass Find peaks Wavelets Window

[11] Stitt, Bertet, and van Walstijn (2016). “Extended Energy Vector Prediction of Ambisonically Reproduced Image Direction at Off- Center Listening Positions”

Results

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Recall: Numerical Simulation #1

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! " Δ ϕ #!

Point source HOA microphone

Key

Listening position

Coloration: Simulation #1

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Distance: rS = 1 m Input order: Lin = 4 Spacing: Δ = 0.5 m

!° "#° $!° %#° &!° '#° (!°

!" #"" !"" #""" !""" #"! " !" #"" #!" $"" # #" #"" "%! ! !"

!"#$%#&'( ()*) !"#$%&'() ((*) !Δ

Weighted Average Method

ϕ =

!° "#° $!° %#° &!° '#° (!°

!" #"" !"" #""" !""" #"! " !" #"" #!" $"" # #" #"" "%! ! !"

!"#$%#&'( ()*) !"#$%&'() ((*) !Δ

Proposed Method

ϕ =

Coloration: Simulation #1 continued

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!!" = ! !!" = " !!" = # !!" = $ !!" = %

!" #"" !"" #""" !""" #"! " !" #"" # #" #"" "$! ! !"

!"#$%#&'( ()*) !"#$%&'() ((*) !Δ

Result: the proposed method achieves negligible coloration for kΔ ≤ 2Lin Proposed method only Distance: rS = 1 m Azimuth: ϕ = 45° Spacing: Δ = 0.5 m

Localization: Simulation #1

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!"#$%&"' ()$* +"$-,-

!"# !"$ !"% !"& !"' !"( !") # ! $! &! *! +! % ' ( ) ## #% #' #(

!""#$ %&#'()* Δ (+) !"#$%&'$(&") *++"+ ϵ (°) !Δ

7.7° 3.9° 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

Localization: Simulation #1 continued

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Result: the proposed method achieves accurate localization for kΔ ≤ 2Lin Proposed method only Distance: rS = 1 m Frequency: f = 1 kHz Averaged over azimuth

=

• Δ ()

ϵ (°) Δ

=

• Δ ()

ϵ (°) Δ

Weighted Avg.

Recall: Numerical Simulation #2

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! " Δ !"#$Δ !"#$Δ (%) (&)

Point source HOA microphone

Key

Listening position

Localization: Simulation #2

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Result: inclusion of invalid microphones can significantly degrade localization Proposed method only Input order: Lin = 4 Frequency: f = 1 kHz Averaged over azimuth

(a) Source position rS = (0.75Δ, 0, 0)

• Δ ()

ϵ (°) Δ

(b) Source position rS = (0.75Δ, 0.75Δ, 0)

• Δ ()

ϵ (°) Δ

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 ≤ 2Lin
• Demonstrated error introduced by “invalid” microphones
• Future work:
• Validate objective predictions
• Minimize spectral coloration

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References

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[1] M. A. Poletti, “Three-Dimensional Surround Sound Systems Based on Spherical Harmonics,” J. Audio Eng. Soc., vol. 53, no. 11, pp. 1004–1025 (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 9468. [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 9421. [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 3306. [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. 299–310 (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. 317–334 (1999).