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Digital Audio Signal Processing Topic-7: Active Noise Control

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Active Noise Control & 3D Audio Marc Moonen Dept. E.E./ESAT, KU Leuven marc.moonen_at_esat.kuleuven.be ... Propagation of acoustic waves is approximately linear. – PowerPoint PPT presentation

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Title: 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

26
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

30
Conclusions
  • Active Noise Control
  • - Feedforward systems (with implicit
    feedback)
  • - Feedback systems (turned into
    feedforward)
  • 3D Audio
  • - Binaural synthesis cross-talk
    cancellation.
  • - Soundfield synthesis
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