Marc Moonen Dept. E.E./ESAT, KU Leuven marc.moonen@esat.kuleuven.be Digital Audio Signal Processing Topic-7: Active Noise Control & 3D Audio Marc Moonen Dept. E.E./ESAT, KU Leuven marc.moonen@esat.kuleuven.be

Lecture-6: Active Noise Control & 3D Audio 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

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 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

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…’

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…’

Feedforward ANC (1) Basic set-up: d C(z) e x W(z) y 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

Feedforward ANC (2) Design problem: d H(z) C(z) e x W(z) y primary 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 C(z) d e W(z) y secondary path primary source x H(z)

Filtered-X LMS (1) d H(z) C(z) straightforward application of LMS : e …does not work here (example C(z)=-1, then steepest ascent instead of steepest descent) C(z) d e W(z) y secondary path primary source x H(z)

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

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) C(z) d e W(z) y secondary path primary source x H(z) C’(z)

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)

Feedforward ANC (3) Additional problem-1: F(z) d C(z) e x W(z) y 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) C(z) d e W(z) y secondary source primary x F(z)

Feedforward ANC (4) Additional problem-2: noise d C(z) e x W(z) y 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 C(z) d e W(z) y secondary source primary x

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.

Feedforward ANC (6) Multiple Error (filtered-X) LMS: L K M 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

Feedback ANC (1) Basic set-up : C(z) = secondary path (see page 6) 1 microphone instead of 2 microphones Applications : active headsets, ear defenders W(z) C(z) primary source d e y secondary source

Feedback ANC (2) Design problem : W(z) C(z) d e y + 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 W(z) C(z) d e y +

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. … d e + W’(z) C(z) y -C’(z)

Feedback ANC (4) d C(z) + e y d W’(z) 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)

Feedback ANC (5) d 1 C(z) e x y 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

Feedback ANC (6) Application : active headsets / ear defenders : d 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

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 virtual source location

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) source location p

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, …)

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

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

Compare to feedforward ANC... y secondary path primary source x H 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

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 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 virtual sound source …

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