Digital Audio Signal Processing Topic-7: Active Noise Control & 3D Audio

1. Digital Audio Signal ProcessingTopic-7:Active Noise Control & 3D Audio Marc Moonen Dept. E.E./ESAT, KU Leuven marc.moonen@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 • Passivenoise control : sound absorbers, …, works well for high frequencies (`centimeter-waves’) • Activenoise control : for low frequencies (e.g. 100 Hz>lambda=3,4m.) • 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 in1936 (!) (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. d H(z) C(z) primary source secondary path e x W(z) y 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. d H(z) C(z) primary source secondary path e x W(z) y 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. d H(z) C(z) primary source secondary path e x W(z) y C’(z) x 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) N=filter length W(Z) L=filter 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. F(z) d C(z) primary source secondary source e x W(z) y 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. d C(z) primary source secondary source e x W(z) y 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. primary source d C(z) secondary source y e W(z) 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. d C(z) + y e W(z) 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. d C(z) + + y e W’(z) -C’(z) 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. virtual source location 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. source location p 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 (>6kHz)) • `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: translation<10cm, rotation<10degrees

26. Compare to feedforward ANC... (see page 6) d H C primary source e secondary path x W y

27. H C primary source secondary path e x W y 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. … virtual sound source … 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. … … virtual sound source 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