1. 3-D Sound and Spatial Audio
MUS_TECH 348
3-D Sound and Spatial Audio

2. Intensity Panning with Loudspeakers

3. sin (ß) / sin (q) = (L - R ) / (L + R)
Stereo Law of Sines
sin (ß) / sin (q) = (L - R ) / (L + R)
Where ß is the angle of the virtual image and
q is the angle of the loudspeaker from center
“Phaser Analysis of Some Stereophonic Phenomena” Ben Bauer 1961

4. By the way, just HOW does panning work?L R
Panning with stereo loudspeakers includes crosstalk!

5. Panning results in amplitude and phase difference!
Consider sine waves! a t a t L R a t a t
Panning results in amplitude and phase difference!

6. + = Consider sine waves! L sin (2p f t) R sin (2p f t)
k (<1) and ø are constant for fixed loudspeaker & listener locations
L sin (2p f t) +
kR sin (2p f t + ø) L
* R --- delayed (ø ) and reduced in gain (k) * t + t = t

7. Consider sine waves! a t a t L R R sin (2p f t) + kL sin (2p f t + ø)
kR sin (2p f t + ø)
What about the resulting IID and ITD?

8. Consider sine waves! R and L affect the IID and interaural phase! a t
( L2 + k2R2 + 2 kLR cos (- ø) )
IID(in decibels) = 10 log
(k2L2 + R2 + 2 kLR cos (- ø) )
L sin(2pft) + R sin(2pft+ ø)
L cos(2pft) + R cos(2pft+ ø)
Interaural phase = arctan
R and L affect the IID and interaural phase!

9. Panning Methods 0.5 amp Amplitude Panning L (C) R position 0.7
Intensity or Power Panning
amp
L (C) R
position

10. Panning Methods Near-field Monitoring: Large-space Monitoring:
Greatest accuracy:
Low Frequencies:
amplitude panning
High Frequencies:
power panning
Large-space Monitoring:
power panning

11. Panning Inaccuracy
High
Low
L (C) R
position

12. How well does panning work in typical multichannel settings like 5.1?
L C R S1 S2 S1 S2 S1 S2 S1 S2

13. ITD / IID
HRTF
For side locations the only change is a cross fading of HRTFs!
Cross fading does not produce proper HRTFs in the middle!
HRTF
only
HRTF
ITD / IID