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

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 www.princeton.edu/3D3A 1

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

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

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

Proposed Method 5

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

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

Proposed Method Unknown HOA signals • Pose as frequency-dependent M · x = y inverse problem • Write translation matrix from √ w 1 T ( − ~ d 1 )     √ w 1 b 1 listening position to each of P √ w 2 T ( − ~ √ w 2 b 2 d 2 ) microphones      · x =     . . .     . . .    • When multiplied by x , should √ w P T ( − ~ √ w P b P d P ) give measured signals Translation Measured HOA matrices signals • Compute regularized pseudoinverse via singular x = V ΘΣ + U ∗ · y value decomposition of M ˜ Least-squares estimate 8

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

Evaluation 10

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

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

Results 13

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

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

Coloration: Simulation #1 continued ! Δ "$! # ! #" !" #"" ! !" = % #"" ! !" = $ !"#$%&'() ( (* ) ! !" = # !" ! !" = " ! !" = ! " !" #"" !"" #""" !""" #" ! !"#$%#&'( ( )* ) Result : the proposed method achieves negligible Proposed method only coloration for k Δ ≤ 2 L in Distance: r S = 1 m Azimuth: ϕ = 45° Spacing: Δ = 0.5 m 16

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: r S = 1 m Input order: L in = 4 Frequency: f = 1 kHz Averaged over azimuth 17

Localization: Simulation #1 continued � Δ � Δ � � � � � � � � �� �� �� �� �� �� �� �� �� �� ������������ ����� ϵ (°) ������������ ����� ϵ (°) �� �� �� �� �� �� Weighted Avg. � �� = � � �� = � � � � � � � ��� ��� ��� ��� ��� ��� ��� ��� ��� ��� ��� ��� ��� � ��� � ����� ������� Δ ( � ) ����� ������� Δ ( � ) Result : the proposed method achieves accurate localization for k Δ ≤ 2 L in Proposed method only Distance: r S = 1 m Frequency: f = 1 kHz Averaged over azimuth 18

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

Localization: Simulation #2 � Δ � Δ � � � � �� �� �� �� � � � � �� �� �� �� �� �� ������������ ����� ϵ (°) ������������ ����� ϵ (°) �� �� ����� ���� �� �� ��� ����� ���� ��� �� �� � � ��� ��� ��� ��� ��� ��� ��� � ��� ��� ��� ��� ��� ��� ��� � ����� ������� Δ ( � ) ����� ������� Δ ( � ) (a) Source position r S = (0.75 Δ , 0, 0) (b) Source position r S = (0.75 Δ , 0.75 Δ , 0) Result : inclusion of invalid microphones can Proposed method only significantly degrade localization Input order: L in = 4 Frequency: f = 1 kHz Averaged over azimuth 20

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: k Δ ≤ 2 L in • Demonstrated error introduced by “invalid” microphones • Future work: • Validate objective predictions • Minimize spectral coloration 21