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

SLIDE 1

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

SLIDE 2

Motivation

SLIDE 3

Motivation

1

SLIDE 4

Motivation

2

SLIDE 5

Motivation

3

SLIDE 6

Measurement Setup

4

SLIDE 7

Time Domain

year(t) = s(t) ∗ hrirear(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.

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SLIDE 8

Spherical Harmonics Domain

year(t) = s(t) ∗

Ω

SHT{hrirear(Ω, t)} · Y m

n (Ω)dΩ .

(2) yl,r(ω) =

∞

n=0

+n

m=−n

˘ Snm(ω) ˘ Hl,r

nm(ω) ,

(3) where Y m

n (Ω) are the spherical harmonics basis functions. 6

SLIDE 9

Order Truncation

Inverse spherical harmonics transform is given as the Fourier series f (Ω) =

N

n=0

+n

m=−n

fnmY m

n (Ω) .

(4)

Bernsch¨ utz, B. (2016). Microphone Arrays and Sound Field Decomposition for Dynamic Binaural Recording.

7

SLIDE 10

Order Truncation

50 100 150 200 250 300 350

Angle in deg

40
35
30
25
20
15
10
5

Amplitude in dB

5 10 20 30

8

SLIDE 11

Problem

SLIDE 12

Order Truncation

102 103 104

f (Hz)

30
25
20
15
10
5

dB Domain CTF difference SH: 3

left right

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SLIDE 13

Order Truncation

102 103 104

f (Hz)

30
25
20
15
10
5

dB Domain CTF difference SH: 8

left right

10

SLIDE 14

Order Truncation

102 103 104

f (Hz)

30
25
20
15
10
5

dB Domain CTF difference SH: 15

left right

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SLIDE 15

Order Truncation - Angle Dependency

102 103 104

f (Hz)

20
10

10 20

dB Rendered difference SH 3; Source: = 0.00, = 1.57

left right

102 103 104

f (Hz)

20
10

10 20

dB Average

12

SLIDE 16

Order Truncation - Angle Dependency

102 103 104

f (Hz)

20
10

10 20

dB Rendered difference SH 3; Source: = 0.79, = 1.57

left right

102 103 104

f (Hz)

20
10

10 20

dB Average

13

SLIDE 17

Order Truncation - Angle Dependency

102 103 104

f (Hz)

20
10

10 20

dB Rendered difference SH 3; Source: = 1.57, = 1.57

left right

102 103 104

f (Hz)

20
10

10 20

dB Average

14

SLIDE 18

Order Truncation - Angle Dependency

102 103 104

f (Hz)

20
10

10 20

dB Rendered difference SH 3; Source: = 1.92, = 1.57

left right

102 103 104

f (Hz)

20
10

10 20

dB Average

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SLIDE 19

Solutions

SLIDE 20

Order Truncation

Assuming a diffuse incident field p(kr0)|N = 1 4π

N
n=0

(2n + 1)|bn(kr0)|2 . (5) The mode strength on the rigid sphere bn(kr0) = 4πin

jn(kr0) − j′

n(kr0)

h′

n(kr0))hn(kr0)

,

(6) where jn is the spherical Bessel function and hn 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

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SLIDE 21

Order Truncation

102 103 104

f in Hz

300
250
200
150
100
50

p in dB pmode

3 7 15 30

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SLIDE 22

Order Truncation

102 103 104

f in Hz

30
25
20
15
10
5

5

p in dB psphere

3 7 15 30

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SLIDE 23

Order Truncation

102 103 104

f in Hz

5 10 15 20 25 30

p in dB Filter

3 7 15

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SLIDE 24

Order Truncation - Angle Dependency

Inverse spherical harmonics transform is given as the Fourier series p(k, Ω) =

N

n=0

+n

m=−n

pnm(k)Y m

n (Ω) .

(7) On the spherical scatterer assuming a plane wave density a(k) p(k, Ω) =

N

n=0

+n

m=−n

anm(k)bn(kr0)Y m

n (Ω) .

(8) In case of a unit amplitude plane wave p(k, Ω) =

N

n=0

+n

m=−n

bn(kr0)[Y m

n (Ωk)]∗Y m n (Ω) ,

(9) with the spherical harmonics addition theorem p(k, Ω)|N =

N

n=0

bn(kr0)2n + 1 4π Pn(cos ∆) . (10)

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SLIDE 25

Order Truncation - Angle Dependency

102 103 104

Hz

20
15
10
5

5 10

dB Nsph = 38 (L)

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SLIDE 26

Order Truncation - Angle Dependency

102 103 104

Hz

20
15
10
5

5 10

dB Nsph = 3 (L)

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SLIDE 27

Order Truncation - Angle Dependency

102 103 104

Hz

20
15
10
5

5 10 15 20

dB Angle compensation filter between orders 3 and 38

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SLIDE 28

Tapering in SH domain

SLIDE 29

Tapering Window

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

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SLIDE 30

Tapering Window

50 100 150 200 250 300 350

Angle in deg

40
35
30
25
20
15
10
5

Amplitude in dB

rect hann

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SLIDE 31

Tapering Window

p(kr0)|N = 1 4π

N
n=0

wN(n)(2n + 1)|bn(kr0)|2 , (11) with the half-sided tapering window wN(n).

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SLIDE 32

Outlook

But how does it sound?

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SLIDE 33

Order Truncation - No Tapering

1 2 3 4 5 6

Azimuth

0.5 1 1.5 2 2.5

Colatitude

1 2 3 4 5 6 7 8 9 10

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SLIDE 34

Order Truncation - Tapering

1 2 3 4 5 6

Azimuth

0.5 1 1.5 2 2.5

Colatitude

1 2 3 4 5 6 7 8 9 10

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SLIDE 35

Order Truncation - No Tapering

10

6 1 1 Colatitude 4 Azimuth 10 2 2 3

10

10

10

6 1 2 Colatitude 4 Azimuth 10 2 2 3

10

10

10

6 1 3 Colatitude 4 Azimuth 10 2 2 3

10

10

30

SLIDE 36

Order Truncation - Tapering

10

6 1 1 Colatitude 4 Azimuth 10 2 2 3

10

10

10

6 1 2 Colatitude 4 Azimuth 10 2 2 3

10

10

10

6 1 3 Colatitude 4 Azimuth 10 2 2 3

10

10

31

SLIDE 37

Order Truncation - No Tapering

50 100 150 200 250

1

1

HRIRs left

50 100 150 200 250

t in samples

0.1

0.1

HRIRs right

t SH5

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SLIDE 38

Order Truncation - Tapering

50 100 150 200 250

1

1

HRIRs left

50 100 150 200 250

t in samples

0.1

0.1

HRIRs right

t SH5

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SLIDE 39

Coloration

50 100 150 200 250 300 350

Angle

1 2 3 4 5 6 7 8 9 10

dB Coloration above 2.5kHz

s_out_t.wav s_out_shN5_no.wav s_out_shN5_order.wav s_out_shN5_taper.wav

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SLIDE 40

Tapering Window

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

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SLIDE 41

Tapering Window

50 100 150 200 250 300 350

Angle in deg

40
35
30
25
20
15
10
5

Amplitude in dB

rect hann

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SLIDE 42

Coloration

50 100 150 200 250 300 350

Angle

2 4 6 8 10 12

dB Coloration above 2.5kHz

s_out_t.wav s_out_shN3_no.wav s_out_shN3_order.wav s_out_shN3_taper.wav

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SLIDE 43

THANK YOU!!

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