Improvements on Higher Order Ambisonics Reproduction in the - PowerPoint PPT Presentation

Improvements on Higher Order Ambisonics Reproduction in the Spherical Harmonics Domain Under Real-time Constraints Christoph Hold , Hannes Gamper September 14, 2018 Microsoft Research, Technical University Berlin

Motivation

Motivation 1

Motivation 2

Motivation 3

Measurement Setup 4

Time Domain y ear ( t ) = s ( t ) ∗ hrir ear (Ω , t ) . (1) With: Ω = (Φ , θ ) Møller, H., Sørensen, M. F., Hammershøi, D., Jensen, C. B. (1995). Head-Related Transfer-Functions of Human-Subjects. JAES. 5

Spherical Harmonics Domain � SHT { hrir ear (Ω , t ) } · Y m y ear ( t ) = s ( t ) ∗ n (Ω) d Ω . (2) Ω + n ∞ � � S nm ( ω ) ˘ ˘ y l , r ( ω ) = H l , r nm ( ω ) , (3) n =0 m = − n where Y m n (Ω) are the spherical harmonics basis functions. 6

Order Truncation Inverse spherical harmonics transform is given as the Fourier series + n N � � f nm Y m f (Ω) = n (Ω) . (4) n =0 m = − n Bernsch¨ utz, B. (2016). Microphone Arrays and Sound Field Decomposition for Dynamic Binaural Recording. 7

Order Truncation 0 5 10 -5 20 30 -10 Amplitude in dB -15 -20 -25 -30 -35 -40 0 50 100 150 200 250 300 350 Angle in deg 8

Problem

Order Truncation Domain CTF difference SH: 3 0 -5 -10 dB -15 -20 -25 left right -30 10 2 10 3 10 4 f (Hz) 9

Order Truncation Domain CTF difference SH: 8 0 -5 -10 dB -15 -20 -25 left right -30 10 2 10 3 10 4 f (Hz) 10

Order Truncation Domain CTF difference SH: 15 0 -5 -10 dB -15 -20 -25 left right -30 10 2 10 3 10 4 f (Hz) 11

Order Truncation - Angle Dependency Rendered difference SH 3; Source: = 0.00, = 1.57 20 left right 10 dB 0 -10 -20 10 2 10 3 10 4 f (Hz) Average 20 10 dB 0 -10 -20 10 2 10 3 10 4 f (Hz) 12

Order Truncation - Angle Dependency Rendered difference SH 3; Source: = 0.79, = 1.57 20 left right 10 dB 0 -10 -20 10 2 10 3 10 4 f (Hz) Average 20 10 dB 0 -10 -20 10 2 10 3 10 4 f (Hz) 13

Order Truncation - Angle Dependency Rendered difference SH 3; Source: = 1.57, = 1.57 20 left right 10 dB 0 -10 -20 10 2 10 3 10 4 f (Hz) Average 20 10 dB 0 -10 -20 10 2 10 3 10 4 f (Hz) 14

Order Truncation - Angle Dependency Rendered difference SH 3; Source: = 1.92, = 1.57 20 left right 10 dB 0 -10 -20 10 2 10 3 10 4 f (Hz) Average 20 10 dB 0 -10 -20 10 2 10 3 10 4 f (Hz) 15

Solutions

Order Truncation Assuming a diffuse incident field � N � p ( kr 0 ) | N = 1 � � (2 n + 1) | b n ( kr 0 ) | 2 . (5) � 4 π n =0 The mode strength on the rigid sphere � j n ( kr 0 ) − j ′ n ( kr 0 ) � b n ( kr 0 ) = 4 π i n n ( kr 0 )) h n ( kr 0 ) , (6) h ′ where j n is the spherical Bessel function and h n the spherical Hankel function of second kind. Ben-Hur, Z., Brinkmann, F., Sheaffer, J., Weinzierl, S., Rafaely, B. (2017). Spectral equalization in binaural signals represented by order-truncated spherical harmonics. The Journal of the Acoustical Society of America 16

Order Truncation p mode 0 -50 -100 p in dB -150 -200 0 3 -250 7 15 30 -300 10 2 10 3 10 4 f in Hz 17

Order Truncation p sphere 5 0 -5 -10 p in dB -15 -20 0 3 7 -25 15 30 -30 10 2 10 3 10 4 f in Hz 18

Order Truncation Filter 30 0 3 7 25 15 20 p in dB 15 10 5 0 10 2 10 3 10 4 f in Hz 19

Order Truncation - Angle Dependency Inverse spherical harmonics transform is given as the Fourier series + n N � � p nm ( k ) Y m p ( k , Ω) = n (Ω) . (7) n =0 m = − n On the spherical scatterer assuming a plane wave density a ( k ) N + n � � a nm ( k ) b n ( kr 0 ) Y m p ( k , Ω) = n (Ω) . (8) n =0 m = − n In case of a unit amplitude plane wave N + n � � b n ( kr 0 )[ Y m n (Ω k )] ∗ Y m p ( k , Ω) = n (Ω) , (9) n =0 m = − n with the spherical harmonics addition theorem N b n ( kr 0 )2 n + 1 � p ( k , Ω) | N = P n (cos ∆) . (10) 20 4 π n =0

Order Truncation - Angle Dependency Nsph = 38 (L) 10 5 0 dB -5 -10 -15 -20 10 2 10 3 10 4 Hz 21

Order Truncation - Angle Dependency Nsph = 3 (L) 10 5 0 dB -5 -10 -15 -20 10 2 10 3 10 4 Hz 22

Order Truncation - Angle Dependency Angle compensation filter between orders 3 and 38 20 15 10 5 dB 0 -5 -10 -15 -20 10 2 10 3 10 4 Hz 23

Tapering in SH domain

Tapering Window 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 24

Tapering Window 0 rect hann -5 -10 Amplitude in dB -15 -20 -25 -30 -35 -40 0 50 100 150 200 250 300 350 Angle in deg 25

Tapering Window � N � p ( kr 0 ) | N = 1 � � w N ( n )(2 n + 1) | b n ( kr 0 ) | 2 , (11) � 4 π n =0 with the half-sided tapering window w N ( n ). 26

Outlook But how does it sound? 27

Order Truncation - No Tapering 0 10 9 0.5 8 7 1 6 Colatitude 5 1.5 4 2 3 2 2.5 1 0 0 1 2 3 4 5 6 Azimuth 28

Order Truncation - Tapering 0 10 9 0.5 8 7 1 6 Colatitude 5 1.5 4 2 3 2 2.5 1 0 0 1 2 3 4 5 6 Azimuth 29

Order Truncation - No Tapering 1 10 10 0 0 -10 0 6 1 4 2 -10 2 3 0 Colatitude Azimuth 2 10 10 0 0 -10 0 6 1 4 2 -10 2 3 0 Colatitude Azimuth 3 10 10 0 0 -10 0 6 1 4 2 -10 2 3 0 Colatitude Azimuth 30

Order Truncation - Tapering 1 10 10 0 0 -10 0 6 1 4 2 -10 2 3 0 Colatitude Azimuth 2 10 10 0 0 -10 0 6 1 4 2 -10 2 3 0 Colatitude Azimuth 3 10 10 0 0 -10 0 6 1 4 2 -10 2 3 0 Colatitude Azimuth 31

Order Truncation - No Tapering HRIRs left 1 0 -1 0 50 100 150 200 250 HRIRs right t 0.1 SH5 0 -0.1 0 50 100 150 200 250 t in samples 32

Order Truncation - Tapering HRIRs left 1 0 -1 0 50 100 150 200 250 HRIRs right t 0.1 SH5 0 -0.1 0 50 100 150 200 250 t in samples 33

Coloration Coloration above 2.5kHz 10 s_out_t.wav 9 s_out_shN5_no.wav s_out_shN5_order.wav 8 s_out_shN5_taper.wav 7 6 dB 5 4 3 2 1 0 0 50 100 150 200 250 300 350 Angle 34

Tapering Window 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1 1.5 2 2.5 3 3.5 4 35

Tapering Window 0 rect hann -5 -10 Amplitude in dB -15 -20 -25 -30 -35 -40 0 50 100 150 200 250 300 350 Angle in deg 36

Coloration Coloration above 2.5kHz 12 s_out_t.wav s_out_shN3_no.wav s_out_shN3_order.wav 10 s_out_shN3_taper.wav 8 dB 6 4 2 0 0 50 100 150 200 250 300 350 Angle 37

THANK YOU!! 38