Soundfield Navigation using an Array of Higher-Order Ambisonics Microphones

1

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

2

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

4

[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

8

M · x = y

x̃ = V⇥⌃+U

⇤ · y

y =

2

6664

pw1b1pw2b2...p

wPbP

3

7775M =

2

6664

pw1T(� ~d1)pw2T(� ~d2)

...pwPT(� ~dP )

3

7775M · x = y

Unknown HOA signals

Measured HOA signals

Translation matrices

Least-squares estimate

Microphone Validity

9

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

10

Numerical Simulations

11

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Simulation #1 Simulation #2

Point sourceHOA 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

13

Recall: Numerical Simulation #1

14

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Point sourceHOA microphone

Key

Listening position

Coloration: Simulation #1

15

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

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Weighted Average Method

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Proposed Method

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Coloration: Simulation #1 continued

16

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Result: the proposed method achieves negligible coloration for kΔ ≤ 2LinProposed method only

Distance: rS = 1 m Azimuth: ϕ = 45° Spacing: Δ = 0.5 m

Localization: Simulation #1

17

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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

18

Result: the proposed method achieves accurate localization for kΔ ≤ 2Lin

Proposed method only Distance: rS = 1 m Frequency: f = 1 kHz Averaged over azimuth

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Recall: Numerical Simulation #2

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Point sourceHOA microphone

Key

Listening position

Localization: Simulation #2

20

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)

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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).