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Digital Audio Signal Processing Lecture 6: Acoustic Feedback Control Toon van Waterschoot/Marc Moonen Dept. E.E./ESAT, KU Leuven toon.vanwaterschoot@esat.kuleuven.be marc.moonen@esat.kuleuven.be

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Outline Introduction Acoustic feedback control Notch-filter-based howling suppression (NHS) Adaptive feedback cancellation (AFC) Conclusion

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Outline Introduction sound reinforcement acoustic feedback Acoustic feedback control Notch-filter-based howling suppression (NHS) Adaptive feedback cancellation (AFC) Conclusion

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Introduction: Sound reinforcement Goal: to deliver sufficiently high sound level and best possible sound quality to audience sound sources microphones mixer & amp loudspeakers monitors room audience

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Linear system model: multi-channel single-channel Will restrict ourselves to the single-channel (= single-loudspeaker-single-microphone) case Introduction: Sound reinforcement

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Assumptions (for now): loudspeaker has linear & flat response microphone has linear & flat response forward path (amp) has linear & flat response acoustic feedback path has linear response But: acoustic feedback path has non-flat response

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Acoustic feedback path response: example room (36 m 3 ) impulse response frequency magnitude response Introduction: Sound reinforcement direct coupling early reflections diffuse sound field peaks/dips = anti-nodes/nodes of standing waves peaks ~10 dB above average, and separated by ~10 Hz

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Desired system transfer function: Closed-loop system transfer function: spectral coloration acoustic echoes risk of instability Loop response: loop gain loop phase Introduction: Acoustic feedback

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Nyquist stability criterion: if there exists a radial frequency for which then the closed-loop system is unstable if the unstable system is excited at the critical frequency , then an oscillation at this frequency will occur = howling Maximum stable gain (MSG): maximum forward path gain before instability desirable gain margin 2-3 dB (= MSG actual forward path gain) Introduction: Acoustic feedback (if G has flat response) [Schroeder, 1964]

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Example of closed-loop system instability: loop gain loudspeaker spectrogram Introduction: Acoustic feedback

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Outline Introduction Acoustic feedback control Notch-filter-based howling suppression (NHS) Adaptive feedback cancellation (AFC) Conclusion

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Acoustic feedback control Goal of acoustic feedback control = to solve the acoustic feedback problem either completely (to remove acoustic coupling) or partially (to remove howling from loudspeaker signal) Manual acoustic feedback control: proper microphone/loudspeaker selection & positioning a priori room equalization using 1/3 octave graphic EQ filters ad-hoc discrete room modes suppression using notch filters Automatic acoustic feedback control: no intervention of sound engineer required different approaches can be classified into four categories

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Acoustic feedback control 1. phase modulation (PM) methods (not addressed here) 2. spatial filtering methods (adaptive) microphone beamforming to reduce direct coupling see Lectures 2&3 3. gain reduction methods (frequency-dependent) gain reduction after howling detection most popular method for sound reinforcement applications 4. room modeling methods adaptive inverse filtering (AIF): adaptive equalization of acoustic feedback path response adaptive feedback cancellation (AFC): adaptive prediction and subtraction of feedback component in microphone signal

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Outline Introduction Acoustic feedback control Notch-filter-based howling suppression (NHS) introduction howling detection notch filter design simulation results Adaptive feedback cancellation (AFC) Conclusion

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Notch-filter-based howling suppression: Introduction gain reduction methods: automation of the actions a sound engineer would undertake classification of gain reduction methods: automatic gain control (full-band (flat) gain reduction) automatic equalization (1/3 octave bandstop filters) NHS: notch-filter-based howling suppression (1/10-1/60 octave filters) NHS subproblems: howling detection notch filter design

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Notch-filter-based howling suppression: Howling detection howling detection procedure: : microphone signal : set of notch filter design parameters

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Notch-filter-based howling suppression: Howling detection howling detection procedure: divide microphone signal in overlapping frames estimate microphone signal spectrum (DFT) select candidate howling components calculate set of discriminating signal features decide on presence/absence of howling : microphone signal : set of notch filter design parameters signal framing frequency analysis peak picking feature calculation howling detection

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Notch-filter-based howling suppression: Howling detection discriminating features for howling detection: acoustic feedback example revisited spectral/temporal features for howling detection?

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howling should only be suppressed when it is sufficiently loud Notch-filter-based howling suppression: Howling detection spectral signal features for howling detection: 1.Peak-to-Threshold Power Ratio (PTPR)

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spectral signal features for howling detection: 1.Peak-to-Threshold Power Ratio (PTPR) 2.Peak-to-Average Power Ratio (PAPR) howling eventually has large power compared to speech/audio Notch-filter-based howling suppression: Howling detection

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spectral signal features for howling detection: 1.Peak-to-Threshold Power Ratio (PTPR) 2.Peak-to-Average Power Ratio (PAPR) 3.Peak-to-Harmonic Power Ratio (PHPR) 4.Peak-to-Neighboring Power Ratio (PNPR) temporal signal features for howling detection 1.Interframe Peak Magnitude Persistence (IPMP) 2.Interframe Magnitude Slope Deviation (IMSD) howling does not exhibit a harmonic structure ( in case of clipping!) Notch-filter-based howling suppression: Howling detection

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spectral signal features for howling detection: 1.Peak-to-Threshold Power Ratio (PTPR) 2.Peak-to-Average Power Ratio (PAPR) 3.Peak-to-Harmonic Power Ratio (PHPR) 4.Peak-to-Neighboring Power Ratio (PNPR) temporal signal features for howling detection 1.Interframe Peak Magnitude Persistence (IPMP) 2.Interframe Magnitude Slope Deviation (IMSD) howling is a non-damped sinusoid, having approx. zero bandwidth Notch-filter-based howling suppression: Howling detection

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spectral signal features for howling detection: 1.Peak-to-Threshold Power Ratio (PTPR) 2.Peak-to-Average Power Ratio (PAPR) 3.Peak-to-Harmonic Power Ratio (PHPR) 4.Peak-to-Neighboring Power Ratio (PNPR) temporal signal features for howling detection 1.Interframe Peak Magnitude Persistence (IPMP) 2.Interframe Magnitude Slope Deviation (IMSD) howling components typically persist longer than speech/audio Notch-filter-based howling suppression: Howling detection

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spectral signal features for howling detection: 1.Peak-to-Threshold Power Ratio (PTPR) 2.Peak-to-Average Power Ratio (PAPR) 3.Peak-to-Harmonic Power Ratio (PHPR) 4.Peak-to-Neighboring Power Ratio (PNPR) temporal signal features for howling detection 1.Interframe Peak Magnitude Persistence (IPMP) 2.Interframe Magnitude Slope Deviation (IMSD) howling exhibits an exponential amplitude buildup over time Notch-filter-based howling suppression: Howling detection

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howling detection as a binary hypothesis test: detection performance: probability of detection probability of false alarm example of detection data set: howling does not occur(Null hypothesis) howling does occur(Alternative hypothesis) o = positive realizations (N P = 166) x = negative realizations (N N = 482) 123456789 0 500 1000 1500 2000 2500 3000 time (s) frequency (Hz) ~ reliability ~ sound quality

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Notch-filter-based howling suppression: Howling detection example of single-feature howling detection criterion: evaluation measures: ROC curve: P D vs. P FA P FA for fixed P D = 95 % criterionP FA PTPR70 % PAPR63 % PHPR37 % PNPR33 % IPMP54 % IMSD40 % T PAPR = dB T PAPR = 54 dB T PAPR = 52 dB T PAPR = 50 dB T PAPR = 32 dB T PAPR = dB

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Notch-filter-based howling suppression: Howling detection improved detection with multiple-feature howling detection criteria: logical conjunction of two or more single-feature criteria design guideline: combine features with high P D, regardless of P FA examples of multiple-feature criteria: PHPR & IPMP [Lewis et al. (Sabine Inc.), 1993] FEP = PNPR & IMSD [Osmanovic et al., 2007] PHPR & PNPR, PHPR & IMSD, PNPR & IMSD, PHPR & PNPR & IMSD [van Waterschoot & Moonen, 2008] single-feature criterion P FA multiple-feature criterion P FA PTPR70 %PHPR & IPMP65 % PAPR63 %FEP24 % PHPR37 %PHPR & PNPR14 % PNPR33 %PHPR & IMSD25 % IPMP54 %PNPR & IMSD5 % IMSD40 %PHPR & PNPR & IMSD3 %

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Notch-filter-based howling suppression: Notch filter design notch filter design procedure: set of notch filter design parameters bank of notch filters transfer function

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Notch-filter-based howling suppression: Notch filter design notch filter design procedure: set of notch filter design parameters bank of notch filters transfer function check active filters notch filter specification notch filter design is a notch filter already active around howling frequency? no? new filter: center frequency = howling frequency yes? active filter: decrease notch gain translate filter specifications into filter coefficients filter index

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Outline Introduction Acoustic feedback control Notch-filter-based howling suppression (NHS) Adaptive feedback cancellation (AFC) introduction closed-loop signal decorrelation adaptive filter design simulation results Conclusion

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Adaptive feedback cancellation: Introduction AFC concept: predict and subtract entire feedback signal component (i.o. only howling component) in microphone signal requires adaptive estimation of acoustic feedback path model similar to acoustic echo cancellation, but much more difficult due to closed signal loop

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Adaptive feedback cancellation: Closed-loop signal decorrelation AFC correlation problem: LS estimation bias vector non-zero bias results in (partial) source signal cancellation LS estimation covariance matrix with source signal covariance matrix large covariance results in slow adaptive filter convergence need decorrelation of loudspeaker and source signal

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Adaptive feedback cancellation: Closed-loop signal decorrelation Decorrelation in the closed signal loop: noise injection time-varying processing nonlinear processing forward path delay Inherent trade-off between decorrelation and sound quality

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Adaptive feedback cancellation: Closed-loop signal decorrelation Decorrelation in the adaptive filtering circuit: adaptive filter delay decorrelating prefilters based on source signal model Sound quality not compromised Additional information required: acoustic feedback path delay source signal model

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Adaptive feedback cancellation: Adaptive filter design LS-based adaptive filtering algorithms: recursive least squares (RLS) affine projection algorithm (APA) (normalized) least mean squares ((N)LMS) frequency-domain NLMS partitioned-block frequency domain NLMS prediction-error-method(PEM)-based adaptive filtering algorithms: joint estimation of acoustic feedback path and source signal model requires forward path delay + exploits source signal nonstationarity available in all flavours (RLS, APA, NLMS, frequency domain, ) 25-50 % computational overhead compared to LS-based algorithms

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Outline Introduction Acoustic feedback control Notch-filter-based howling suppression (NHS) Adaptive feedback cancellation (AFC) Conclusion

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Conclusion: Acoustic feedback control methods phase modulation methods: suited for low-gain applications such as reverberation enhancement spatial filtering methods: removal of direct coupling if multiple microphones are available gain reduction methods: notch-filter-based howling suppression popular for sound reinforcement applications accurate howling detection is crucial for sound quality and reliability reasonable MSG increase (up to 5 dB) can be attained room modeling methods: adaptive feedback cancellation upcoming method as computational resources become cheaper decorrelation in adaptive filtering circuit for high sound quality MSG increase up to 20 dB is generally achieved

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Literature review paper: T. van Waterschoot and M. Moonen, Fifty years of acoustic feedback control: state of the art and future challenges, Proc. IEEE, vol. 99, no. 2, Feb. 2011, pp. 288-327. phase modulation: J. L. Nielsen and U. P. Svensson, Performance of some linear time-varying systems in control of acoustic feedback, J. Acoust. Soc. Amer., vol. 106, no. 1, pp. 240254, Jul. 1999. spatial filtering: G. Rombouts, A. Spriet, and M. Moonen, Generalized sidelobe canceller based combined acoustic feedback- and noise cancellation, Signal Process., vol. 88, no. 3, pp. 571581, Mar. 2008. notch-filter-based howling suppression: T. van Waterschoot and M. Moonen, Comparative evaluation of howling detection criteria in notch-filter-based howling suppression, J. Audio Eng. Soc., Nov. 2010, vol. 58, no. 11, Nov. 2010, pp. 923-940. T. van Waterschoot and M. Moonen, A pole-zero placement technique for designing second-order IIR parametric equalizer filters, IEEE Trans. Audio Speech Lang. Process., vol. 15, no. 8, pp. 25612565, Nov. 2007. adaptive feedback cancellation: G. Rombouts, T. van Waterschoot, K. Struyve, and M. Moonen, Acoustic feedback suppression for long acoustic paths using a nonstationary source model, IEEE Trans. Signal Process., vol. 54, no. 9, pp. 34263434, Sep.2006. G. Rombouts, T. van Waterschoot, and M. Moonen, Robust and efficient implementation of the PEM-AFROW algorithm for acoustic feedback cancellation, J. Audio Eng. Soc., vol. 55, no. 11, pp. 955966, Nov. 2007. T. van Waterschoot and M. Moonen, Adaptive feedback cancellation for audio applications, Signal Process., vol. 89, no. 11, pp. 21852201, Nov. 2009.