Digital Audio Signal Processing Topic-7: Active Noise Control

1
Digital Audio Signal ProcessingTopic-7 Active
Noise Control 3D Audio

• Marc Moonen
• Dept. E.E./ESAT, KU Leuven
• marc.moonen_at_esat.kuleuven.be

2
Lecture-6 Active Noise Control 3D Audio

• Active Noise Control
• General set-up
• Feedforward ANC Filtered-X LMS
• Feedback ANC
• Reference S.J.Elliott P.A.Nelson, Active
  Noise Control, IEEE Signal Processing Magazine,
  October 1993, pp 12-35
• 3D Audio
  
• Head related transfer functions(HRTF)
• Binaural synthesis
• Cross-talk cancellation

3
Active Noise Control - Intro

• Passive noise control sound absorbers, ,
• works well for high
  frequencies (centimeter-waves)
• Active noise control for low frequencies (e.g.
  100 Hzgtlambda3,4m.)
• General set-up
• - ANC works on the principle of destructive
  interference between the sound field generated by
  the primary (noise) source and the sound field
  due to secondary source(s), whose output can be
  controlled

aim generate quiet at error microphone
4
Active Noise Control - Intro

• Secondary source(s)
• mostly loudspeakers
• sometimes mechanical shakers (excitation of
  structural components)
• Signal processing task generation/control of
  electrical signal(s) to steer secondary source(s)
• Two approaches will be considered
• Feedforward ANC solution based on filtered-X
  LMS
• Feedback ANC see also control courses
• PS First ANC Patent in 1936 (!) (Paul Lueg)
• describes basic idea of measuring a sound
  field with a
• microphone, electrically manipulating the
  resulting signal and then
• feeding it to a secondary source

5
Active Noise Control - Intro

• Destructive interference relies on superposition
  linearity
• Propagation of acoustic waves is approximately
  linear.
• Non-linearity may be due to loudspeakers
  (secondary sources)
• After destructive interference at main
  frequency, harmonics generated
• by loudspeakers may become distinctly
  audible.
• Destructive interference at one point, may imply
  constructive interference at other points
• secondary source to be placed close to error
  microphone, so that only modest secondary signal
  is required, and hence points further away from
  secondary source are not affected. Produce zone
  of quiet near the error microphone (e.g. 10dB
  reduction in zone approx (1/10).lamba)

shut up
quiet
secondary
SHUT UP
6
Feedforward ANC (1)

• Basic set-up
• C(z) secondary path acoustic path from
  secondary source to error microphone, including
  loudspeaker and microphone characteristic. C(z)
  can be modeled/identified, based on training
  sequences, etc. (calibration)
• PS feedback in filter coefficient adaptation path

d
C(z)
primary source
secondary source
e
x
W(z)
y
7
Feedforward ANC (2)

• Design problem
• given (?) secondary path C(z), design W(z) that
  minimizes E(z)
• ideal solution is W(z)-H(z)/C(z)
  H(z) generally unknown

8
Filtered-X LMS (1)

• straightforward application of LMS
• does not work here
• (example C(z)-1, then steepest ascent
  instead of steepest descent)

9
Filtered-X LMS (2)

• This would have been a simpler problem (swap C
  and W)
• ...allowing for straightforward application of
  LMS, with filtered x-signal
• Only time-invariant linear systems commute, hence
  will require slow adaptation of W(z) (see page
  11)

d
x
H(z)
C(z)
e
W(z)
y
10
Filtered-X LMS (3)

• filtered-X LMS scheme swapping of C and W in
  adaptation path (not in filtering path)
• with C(z) an estimate of C(z)
• PS H(z) unknown and not needed for adaptation
  (like in AEC)

11
Filtered-X LMS (4)

• Filtered-X LMS convergence (empirical result)
• Nfilter length W(Z)
• Lfilter length C(z)
• Stability also affected by the accuracy of the
  filter C(z) modeling the true secondary path
  C(z).
• Found to be surprisingly robust to errors in
  C(z)...
• (details omitted)

12
Feedforward ANC (3)

• Additional problem-1
• Feedback from secondary source (loudspeaker) into
  reference microphone.
• This is an acoustic echo cancellation/feedback
  problem
• Fixed AFC based on model of F(z), obtained
  through calibration, is easy
• Adaptive AFC is problematic (combination of 2
  adaptive systems)

13
Feedforward ANC (4)

• Additional problem-2
• Additive noise in error microphone (e.g. due to
  air flow over microphone, etc.)
• Cancellation of primary source signal corrupted
  by noise, similar to near-end noise/speech in AEC

noise
14
Feedforward ANC (5)

• Extensions multiple reference signals/multiple
  secondary
• sources/multiple error
  signals
• Applications airplane/car cabin noise control,
  active vibration control,...
• Needs generalization of Filtered-X algorithm,
  where coefficients of control filters are adapted
  to minimize the sum of the mean square values of
  the error signals.

15
Feedforward ANC (6)

• Multiple Error (filtered-X) LMS
• K reference signals
• M secondary sources
• L error microphones
• MxL different secondary paths between M secondary
  sources and L error microphones
• all K reference signals are filtered (cfr
  filtered-X) by all MxL secondary path models,
• to generate collection of KxMxL filtered
  reference signals, which are input to the
  adaptive filter
• etc..

L
K
M
16
Feedback ANC (1)

• Basic set-up
• C(z) secondary path (see page 6)
• 1 microphone instead of 2 microphones
• Applications active headsets, ear defenders

17
Feedback ANC (2)

• Design problem
• given C(z) design W(z) (feedback control) such
  that E(z) is minimized
• For flat C(z)Cnt W(z)-A for large A (like
  in an opamp)
• For general C(z) see control courses

18
Feedback ANC (3)

• An interesting feedback controller is formed as
  follows
• with C(z) is an estimate of C(z) and
  W(z) yet to be defined.
• Note that if C(z)C(z), then W(z) is fed
  by d (!), i.e.

19
Feedback ANC (4)

• Note that if C(z)C(z), then W(z) is fed by d
  (!), i.e.
• which means the feedback system has been
  transformed
• into a feedforward system, similar to
  page 12..

d
C(z)
e
y
d
W(z)
20
Feedback ANC (5)

• In the set-up of page 12, this is
• with H(z) 1, and for C(z) containing pure delay,
  this means W(z) must act as a predictor for d.
• Adaptation of W(z) based on filtered-X algorithm

d
1
C(z)
primary source
secondary path
e
x
W(z)
y
21
Feedback ANC (6)

• Application active headsets / ear defenders
• 10-15dB reduction can be achieved for frequencies
  30-500Hz
• Problem variability of secondary path (headsets
  worn by different people, or worn in different
  positions by the same person, etc.)
• Headset can also be used to reproduce a useful
  signal u (communications signal, music, ..)
  electrically subtract u from error microphone
  signal

d
C(z)

Prove it !

y
-u
W(z)
e
22
3D Audio

• Virtual acoustic displays
• systems that can render sound images
  positioned arbitrarily around
  a listener.
• Two approaches
• Acoustic soundfield synthesis
• reproduce original soundfield everywhere,
• with large number of transducers.
• Suitable for multiple listeners.
• Binaural audio
• reproduce original soundfield at
• (2) eardrums, with headphones
• or -at least stereo- loudspeakers
• Suitable for single listener

23
Head Related Transfer Function (HRTF)

• HRTF is acoustic transfer function from a
  specific sound location to the eardrum, and
  describes diffraction of sound by the torso, head
  and external ear
• HRTFs differ significantly across subjects
  (especially for high frequencies (gt6kHz))
• average HRTFs measured on mannequins
• Applications use HRTF data base (HRTF for each
  position)

24
Binaural Synthesis

• For source X(z) to be virtually placed at
  position p, signals to be delivered at left/right
  eardrums are
• multiple sources
• referred to as binaural signal, because it
  would be suitable for headphone listening.
  
  Head-phone reproduction (with
  non-individualized HRTFs) often suffers from
  in-head localization, front-back reversals, ...
• TFs may include desired room acoustics (e.g.
  concert hall, )

25
Cross-talk Cancellation

• To correctly deliver the binaural signal to the
  listener, the signals must be equalized, to
  compensate for transmission paths from
  loudspeakers to eardrums. Transmission path
  inversion is referred to as cross-talk
  cancellation, as it involves cancellation of
  unwanted cross-talk from each speaker to the
  opposite ear.
• A_LL is HRTF from
  left speaker to left eardrum,
• 
  should also include actual room acoustics.
• PS Channel
  inversion, see Topic-6
• 
  (easier with e.g. 3 loudspeakers for 2 ears)
• PS
  Equalization zone (sweet spot) typically
• 
  small translationlt10cm, rotationlt10degrees

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Compare to feedforward ANC...

• (see page 6)

d
H
C
primary source
e
secondary path
x
W
y
27
Compare to feedforward ANC...

• Adaptive ?
• head movement tracking (e.g. video-based)
  compensation, provides
• larger equalization zone
• dynamic localization cues (by maintaining
  stationary virtual sources during head motion)
• error signal only available during calibration,
  hence difficult to compensate for variations in
  acoustic channels

28
Sound Field Synthesis

• Huygens principle
• Synthesize sound field in a listening area,
  based on secondary sources
• (loudspeakers) on an enclosure of listening
  area, playing back recorded
• (with microphones on the same enclosure)
  sequences

29
Sound Field Synthesis

• Huygens principle
• This may be realized as a multichannel ANC
  system which then allows for an equalization of
  the actual listening room, as well as a
  reproduction of a virtual listening room

• Multi-channel extension of p. 25-26
• H(z) contains L (virtual) acoustic TFs from
  virtual sound source to mics
• C(z) contains MxL (real) acoustic TFs from
  loudspeakers to mics
• M loudspeakers
• L microphones

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Conclusions

• Active Noise Control
• - Feedforward systems (with implicit
  feedback)
• - Feedback systems (turned into
  feedforward)
• 3D Audio
• - Binaural synthesis cross-talk
  cancellation.
• - Soundfield synthesis