Active Noise Control Headphones

Andre Cerqueira, Paulo Lopesandre.cerqueira@ist.utl.pt

Instituto Superior Tecnico, ULisboa, Lisboa, Portugal

November 2016

Abstract

In acoustic active noise control (ANC), an unwanted noise is acquired by a microphone, processed andan ”anti-noise”, with the opposite phase from the original noise, is emitted by a loudspeaker. The anti-noise is superimposed to the original signal and destructive interference occurs. This paper presentsthe design, implementation and results of an adaptive ANC headphone system. A TMS320C6713floating-point digital signal processor was used as the controller. Various algorithms were employed andperformance has been evaluated and compared between them and with reported results in the literature.Keywords: Active Noise Control (ANC), ANC Headset, Adaptive ANC systems, Digital signalprocessing, LMS Algorithm

1. IntroductionEarmuffs, using passive techniques, are usually usedas personal devices to attenuate noise in transporta-tion, industry etc. However, these compact andlight devices perform better for short wavelengthnoise than for long wavelength noise, i.e. low fre-quency noise. Active noise control (ANC) was in-troduced as a solution to attenuate low frequencynoises, generally bellow 500 Hz. An ANC systemcombines a secondary noise (anti-noise) of oppositephase with the primary noise (unwanted noise), re-sulting in cancellation of both noises, as seen in Fig-ure 1. However, ANC does not perform well for highfrequency noises so, both passive and active tech-niques are used to complement each other in orderto achieve better noise-cancelling results [8]. AnANC headset is an example of application wherethis is employed.

Figure 1: Active noise cancellation concept.

A generic ANC system, seen in Figure 2 is com-posed of an error microphone, to capture the noiseresulting from the superposition, a loudspeaker asthe anti-noise source, a reference microphone to giveadvanced information about the noise, in feedfor-ward systems, and a controller to process the sig-nals.

Most commercial headsets are based on an ana-

Figure 2: Basic blocks of a feedforward ANC sys-tem.

logue filter controller [3]. Their use is advantageousfor their stability, low system delay, low power con-sumption, small hardware size, simple control al-gorithm and good attenuation of random and im-pulse noises (broadband noise)[8]. However, theyare only applicable to linear time-invariant systemsand are hard to design for multiple input, multipleoutput systems [4]. For most ANC applications,the physical system may have time varying acous-tic and environmental characteristics thus the useof an adaptive controller is desired, to model thesevariations.

Adaptive controllers are generally implementedas adaptive filters in digital signal processors. Theseare digital filters whose coefficients are adjustedby an adaptive algorithm. Due to these system’sself-optimizing and tracking capabilities, they haveimproved performance in a larger bandwidth over

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fixed controllers with periodic and tonal noises (nar-rowband noise). Also, they are able to control mul-tiple input and multiple output systems (multichan-nel systems). However, they are digital so the de-lays of the A/D and D/A converters are usuallyhigh, therefore their performance while cancellingbroadband noise is inferior to fixed controllers.

The ideal result of ANC is no sound at all but, inreality, the actual noise cancellation depends on theaccuracy of the data processing algorithm (calcula-tions) to determine and synthesize the anti-noiseand on the characteristics of the system. To im-prove those, new algorithms, hardware and systemconfigurations should be developed and tested. Astable system is difficult to obtain for adaptive con-trollers, since there are multiple sources of instabil-ity for a ANC algorithm such as modelling errors,zeroes in inverse models, over driven systems, i.e.noises too low that exceeds the numerical range ofa system.

One recent design is an ANC headset systememploying both fixed controller and adaptive con-troller. The adaptive controller would reduce pe-riodic signals while the fixed would control broad-band signals [10, 7].

2. BackgroundIn this section, the theoretical background neces-sary to understand the work is presented, namelythe Least Mean Squares (LMS) algorithm, Filtered-X LMS (FxLMS) for a feedforward and feedbackANC system and its variations to solve the prob-lem of secondary path modelling error.

2.1. Types of ANC systemsActive headsets can be interpreted as a problemof noise propagating in ducts, since plane waves inducts and the sound field in a ear cup are both one-dimensional problems, thus enabling good results tobe achieved with a single-channel control system [4].For multi-dimensional noise fields it is necessary toemploy a multiple-channel system.

There are two main configurations for ANC sys-tems: feedback and feedforward. In addition, feed-back types may be further classified into analogue(fixed) and digital (adaptive), depending on thecontroller used. Fixed controllers and multiple-channel systems are outside of the scope of thiswork.

Figure 3 illustrates a single channel feedforwardsystem. It is composed by a controller, two mi-crophones (reference and error) and a loudspeaker.It is the only configuration capable of cancellingbroadband noise if the causality and high coherenceconditions are met.

To ensure causality, the distance from the ref-erence microphone to the error microphone shouldbe greater than the distance from the secondary

Figure 3: Single-channel feedforward ANC systemin a duct.

source to the error microphones. Also, the propa-gation time between the reference sensor and thesecondary source should be larger than the timethe controller takes to generate the anti-noise at theloudspeaker. To achieve high coherence between thereference signal and the primary noise, the referencemicrophone should be close to the noise source, inorder to reduce the amount of ambient noise cap-tured by the microphone. There can be acousticfeedback between the reference microphone and thesecondary source in feedforward systems, but thatshould be low in headset systems.

Figure 4: Single-channel feedback ANC system ina duct.

Adaptive feedback systems are composed of anerror microphone and a secondary source. Sincethere is no reference microphone the reference sig-nal has to be estimated by the system. Therefore,it can only cancel narrowband noise by exploitingtheir predictability. However, they only need onemicrophone and good references are hard to getand therefore are the most used conguration forheadsets.. The only design constraint is the choiceand positioning of the loudspeaker and error micro-phone to improve stability and noise reduction.

2.2. Adaptive ControllerANC can be seen under the system identificationframework as seen in Figure 5.

It works by modelling the primary path P (z),from the reference microphone to the error micro-phone, with an adaptive filter W (z), composed of adigital filter and an adaptive algorithm. The algo-rithm is given a reference signal x(n), already excit-ing P (z), to excite the adaptive model W (z). Theadaptive algorithm adjusts the filter coefficients in

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Figure 5: Adaptive system identification [8].

order to minimize the error signal e(n), computedwith the difference between the physical systemresponse d(n) and adaptive model response y(n).When e(n) has been minimized, the adaptive modelideally reproduces P (z), implying that y(n) = d(n).

The digital filter structure and the adaptive al-gorithm depend on the application requirements.The structure can be (transversal) finite impulse re-sponse (FIR), (recursive) infinite impulse response(IIR), lattice, among others. This work focuses onthe Least Mean Squares (LMS) algorithm, howeverone of its variations, the Normalized LMS (NLMS),was used.

The LMS algorithm [2] updates a FIR filter coef-ficients with

w(n+ 1) = w(n) + µe(n)x(n), (1)

where µ is the step size, w(n) is the filter coefficientsvector and x(n) is the filter input vector, both attime instant n. In order for this algorithm to bestable µ should verify

0 < µ <2

LPx, (2)

where L is the adaptive filter length and Px thepower of the reference signal.

The stability condition of the LMS depends onx(n). That inconvenience can be defeated by nor-malizing µ with respect to an estimate of the refer-ence signal power, resulting in The NLMS algorithm3.

w(n+ 1) = w(n) +µe(n)x(n)

Px(n). (3)

where . denotes estimate. Px is computed with thesquared euclidean norm, for NLMS algorithms as inthe following expression

Px(n) = ‖x(n)‖2 =

L−1∑l=0

x2(n− l). (4)

This algorithm is faster than the ordinary LMS andit is convergent if the following condition on µ issatisfied.

0 < µ < 2, (5)

Another modified version of the LMS was used. Itwas the Leaky-LMS where a leakage factor λ tendsto bias each coefficient toward zero. The principleof this method is similar to adding white noise tothe input signal, prior to the adaptive filter [8]. Ittakes the form

w(n+ 1) = λw(n) + µe(n)x(n), (6)

where λ is the leakage factor with 0 < λ ≤ 1. Thevalue of the leakage factor is in general determinedon an experimental basis, as a compromise betweenrobustness and loss of performance of the adaptivefilter, due to the white noise addition. Usually agood starting point is a leakage factor slightly lessthan 1.

2.3. ANC AlgorithmsIn a real ANC system, the error signal is not com-puted but is obtained by sampling the residualacoustic pressure resulting from the acoustic su-perposition of the noise and anti-noise. Therefore,in the path from the control signal y(n) to the er-ror signal e(n), the devices have transfer functionswhich alter y(n). This is called the secondary pathS(z) and the LMS algorithm should be modified toassure the system convergence.

The filtered-x LMS (FxLMS), illustrated in Fig-ure 6, is one approach to compensate for the sec-ondary path effects [8]. It filters the reference signalx(n) with an estimate of the secondary path trans-fer function S(z) and inputs it in the NLMS alongwith the error signal. Therefore, an estimate of thesecondary path transfer function must be availablefor the FxLMS algorithm.

Figure 6: Block diagram of ANC system using theFxLMS algorithm [4].

The modelling of the secondary path transferfunction is also a system identification problem.This time an internally generated white noise isused as a reference signal to construct the modelS(z), during an initial stage. At the end of thetraining interval, the estimated model S(z) is fixedand used for ANC operation. This is called the off-line modelling technique, and it should be used ifS(z) is time-invariant. Even then, slight changesin the environment during system operation mayhappen which may lead the adaptive algorithm toinstability if the phase difference between S(z) and

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S(z) has an excess of 90◦. To solve this problemthere, are two approaches one can take: to blocknoise control for frequencies whose phase error ex-ceeds 90◦ more frequently; use the on-line modellingtechnique, usually employed in time varying sec-ondary paths.

Adaptive on-line modelling of the secondary pathshould be used when S(z) varies continuously inreal time. S(z) can be either occasionally or con-tinuously estimated and the most recent estimateS(z) used in the weight update of the control fil-ter W (z). Provided that S(z) changes slowly, thecontroller adaptation and secondary-path estima-tion functions can be considered separately. Twomethods as generally used, the overall modellingalgorithm (OMA) and the additive random noisealgorithm.

Figure 7: Block diagram of the feedback BMFxLMSalgorithm.

Two FxLMS variations, which employ the ap-proaches for the secondary path modelling errormentioned above, were used in this work. The feed-back band-limited Modified FxLMS (BMFxLMS)[5], depicted in Figure 7, turns off the noise con-trol by filtering out problematic frequencies of theprimary noise d(n), thus avoiding the instability as-sociated to them. The frequencies where the mod-elling error is more frequent can be determined witha series of off-line modelling runs and computing themaximum phase difference between the estimates.

The MFxLMS is employed to obtain the electri-cal model of the noise cancelling because an acousticsignal cannot be electrically filtered. This is done byestimating the primary noise, adding an estimate ofthe anti-noise y′(n) to the error signal e(n). Then,an estimate of the error signal, called modified errorem(n), is obtained with the difference between the

primary noise estimate d(n) and the output of thefiltered-x signal filtered by the current control filter.Now, it is possible to filter the reference signal x(n)

and d(n) by a bandpass filter F (z), thus achievingthe band limiting. This algorithm was implementedfor a feedback configuration, by using d(n) as a ref-erence signal, to later compare it with the feedback

FxLMS.The Mirrored MFxLMS [6], seen in Figure is a

variation of the MFxLMS algorithm, with the OMAembedded in the algorithm for on-line modelling ofthe primary and secondary paths. It is stable evenwith incorrect secondary path models and dealsvery well with sudden changes. Instead of obtain-ing the electrical model of the noise cancellation asthe regular MFxLMS, it passes the reference signalthrough the primary path estimate P (z) obtaining

the primary noise estimate d(n).

Figure 8: Block diagram of the MMFxLMS algo-rithm [6].

3. System architecture3.1. HardwareThe developed system hardware is composed of acommercial ANC headset, the ATH-ANC1 Quiet-Point r, which had its control circuit removed,in order to use its microphones and loudspeak-ers. A development board, the TMS320C6713 DSPstarter kit (C6713 DSK), Spectrum Digital, housinga TMS320C6713 floating-point digital signal pro-cessor (DSP) from Texas Instruments, was used asthe substitute controller. The programs are down-loaded to the DSK and the data is uploaded fromthe DSK with USB, through a JTAG emulator, toa Personal Computer.

The line-level channels were used as input andoutput of the board, meaning that no pre-amplifiersnor power amplifiers were available. So, a printedcircuit board (PCB) containing the microphones’biasing, the microphones’ pre-amplifiers, the poweramplifiers to drive the loudspeakers and a powercircuit to supply these circuits was produced. Inorder to implement the feedforward configuration,a reference microphone had to be assembled andthe DSK AUDIO4 daughtercard, from EducationalDSP, LLC, was installed in the development boardto expand the number of channels of the C6713DSK. Then, the reference microphone biasing andpre-amplifier circuits were mounted on a bread-board. The analogue board developed is picturedin Figure 9.

The DSK AUDIO4 daughtercard contains two16 bit Coder Decoder (CODEC), each one with a

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Figure 9: Analogue Circuit Developed.

stereo A/D converter (ADC) and a D/A converter(DAC). The maximum input and output of bothdevices is 1 Vrms. The error microphones have anestimated sensitivity of 13.2mV/Pa, and the pre-amplifiers have a gain of AVpre

= 55, thus allow-ing to acquire noises with 2 Pa sound pressure,the maximum noise considered, without saturat-ing the channel. The power amplifier has a gain ofGv = 0.12 outputting enough power for the loud-speakers to cancel a 2 Pa noise. The reference mi-crophone pre-amplifier gain value was determinedexperimentally, to observe its impact on noise can-celling performance. The output of the error mi-crophones pre-amplifiers were connected to the line-input of CODEC0 and input of the power amplifierconnected to the line-output of the CODEC0. Theoutput of the reference microphone pre-amplifierwas connected to the line-input of CODEC1.

A diagram with the components of the systemhardware is depicted in Figure 10.

Figure 10: Diagram of ANC Headset System Hard-ware.

The error and reference signals were acquired ata sampling rate of Fs = 16kHz.

3.2. SoftwareThe software was developed in Code Composer Stu-dio software suite, version 6.1.0. All the programswere implemented in C-language.

Multi-rate signal processing was used to obtainthe low delay of high sampling rates and the highprocessing time, i.e. the time spent by the processordoing the ANC algorithm computations, and loweradaptive filter order of low sampling rates. The 16kHz sampling rate of the CODECs was decimatedto the 2 kHz operating frequency of the ANC algo-rithms operated, meaning a conversion factor of 8was used. The anti-aliasing/anti-image filters usedwere 161st order lowpass FIR filters with 500 Hzas cut-off frequency and 1000 Hz stopband cornerfrequency, with low ripple.

FxLMS algorithm was implemented for bothfeedforward and feedback system. For feedbackFxLMS, the reference signal was synthesized byadding an estimate of the anti-noise y′(n) = y(n) ∗s(n) to the error signal, obtaining a primary noiseestimate which was used as the reference signal. Itused NLMS with the power of the filtered-x as anormalizing factor.

Off-line secondary path estimation also used theNLMS, with the step-size µs = 0.01 normalized bythe power of the internally generated white noise,the training signal. This training signal was usedto achieve fast convergence of the off-line modellingalgorithm.

BMFxLMS algorithm uses the modified error sig-nal, with the primary noise estimate band limited,and filtered-x signal also band limited as the NLMSinput. The normalizing factor was the bandlimitedfiltered-x power. The phase error was found to beabove 90◦ for frequencies under 80 Hz. The bandlimiting filter was implemented using a linear phaseFIR filter. It had cut off frequencies of 100 and 500Hz and stopband corner frequencies of 25 and 900Hz and relatively high ripple comparing to the dec-imator and interpolator filters. The resulting filterwas a 60th order bandpass filter.

The MMFxLMS algorithm [6] was implementedin C-language.

The step sizes, filter lengths and leakage factorsof all algorithms were determined experimentallyto achieve the best performance in an experimentexplained in the following section.

4. Results

Various real-time tests were performed to under-stand the capabilities of the system. All the ex-periments had a user wearing the headset and thedata was acquired by plotting the systems signals inthe graphing tool of CCS, exporting that data andprocess it in MATLAB. The secondary paths of thesystem were characterized, with the secondary pathmodelling error being estimated. Then each algo-rithm went through a process of changing varioussystem parameters, with the resulting performanceassessed.

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4.1. Secondary path characterizationThe parameters, amplifier gains, step-sizes, sam-pling frequency, etc., used at the time of the mea-surements presented in this subsection were not theones in the final system. Nevertheless they are use-ful to make some conclusions.

Audio system measurementsAfter the assembly of the system hardware, i.e.

the stereo headset, DSK board and analogue am-plifier circuit, some of the systems audio character-istics were measured to know to what extent thehardware affects the system performance.

The electrical crosstalk of the DSK was studied.It measured the introduction of electrical noise inone channel, when another channel is excited by asignal. More specifically, the DAC emitted a signalto drive the loudspeaker and the signal sampled bythe ADC was observed. There was no considerableelectrical crosstalk between the channels. However,these results had little significance because the ana-logue circuit was not included in the measurement.

To study the non-linear distortion, the off-linesecondary path modelling had the training sig-nal maximum amplitude increased with the values{5000, 10000, 15000, 20000}. Each run used a valueand the resulting error signal power would be ob-served. If, with each variation of input power, theoutput power does not increase in the same way,there are non-linearities present in the circuit. Itwas observed a linear relationship between the in-put and output powers except for the lowest digitalgain used, Gd = 5k, which exhibited high non lin-earity for low power signals.

(a) Left Channel (b) Right Channel

Figure 11: Secondary path Input-Output linearity.

To determine the total harmonic distortion(THD), a sinusoidal signal, with frequencies f ∈{50, 75, 100, 250, 500, 750, 1000}Hz for each run,was input in the secondary path and the outputTHD, using the harmonics of the input signal fre-quency, was computed. A linear system with a sinu-soidal signal as input has always a sinusoidal signalwith the same frequency at the output. THD is ameasurement of the extent of non-linear distortion.As seen in Figure 12, frequencies below or equal to100 Hz had THD between 1% and 2%. The rest of

Figure 12: Total harmonic distortion of the sec-ondary path.

the frequencies had THD below 1%. The THD re-sults were found to be satisfactory because 1% dis-tortion will be only noticeable for noise cancellinglevels close to 40 dB, which is a great deal more thanwhat is expected for the attenuation performance ofthis system.

4.2. Secondary path off-line modelling

To learn about the off-line secondary path mod-elling algorithm performance, 100 runs of the al-gorithm were realized. Then the phase error be-tween the secondary path and the estimates wascomputed. It should be noted that the samplingfrequency used for these measurements

Figure 13 shows the acquired impulse responses.Each line represents an estimate of the secondarypath. It can be seen that there is great precisionin modelling the delay of the secondary path, i.e.the large peak, because on that point the estimatesare not spread. Thus, one can conclude that thereis a big possibility of the algorithm accurately esti-mating the secondary path delay. However there isa big spread on the signal segment after the peakwhich may result in instability in the system.

Figure 13: Estimated secondary path impulse re-sponses.

Figure 14 shows that there is a big variation ofphase on the lower end of the spectrum. Morespecifically, approximately under 80 Hz the phaseerror is above 90◦ thus, at these frequencies the sys-tem should be more prone to instability or at leastslower convergence. This is was expected because

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(a) Maximum difference between the secondarypath estimates phase.

(b) Detail on the phase error plot of the sec-ondary path estimates.

Figure 14: Phase error of the secondary path esti-mates.

at low frequencies the secondary path has small am-plitude therefore the signal to noise ratio is low inthese frequencies.

4.3. Algorithm performance evaluation

The experimental setup for the parameter optimiza-tion is depicted in Figure 15. This setup was usedfor all the algorithms and the presented distanceswere used in an effort to meet the causality con-dition and high coherency condition. Even thoughit depicts a feedforward system, the reference mi-crophone was turned off when using feedback al-gorithms. The noise source utilized was a PioneerXR-NM1 stereo system.

For each algorithm a good combination of pa-rameter values, which gave good performance, wasfound. Then that set of parameters was used invarious tests where the primary noise was changed.

Experimental parameter optimization

In this procedure the system parameters weremanipulated to achieve the best possible perfor-mance. The parameters to be set were the stepsize µ, the leakage factor λ, the adaptive filterslength Lw = Ls and the reference microphone pre-amplifier gain AVref

. A sinusoidal noise with 100 Hz

Figure 15: Experimental setup of the performanceevaluation.

was used a the primary noise. Two levels of soundpressure were used to test the performance at highsound pressure levels and low sound pressure levels.

The sampling frequency was also varied not withoptimization in mind but to see how the perfor-mance varied with it. The sampling frequenciestested were 16 kHz without decimation, 8 kHz dec-imated from 48 kHz and 2 kHz decimated from 16kHz.

Data was gathered while varying one of thesevariables and holding all others at a constant valueto best isolate its effect on the system. Performancewas assessed by observing 4 different performancemeasures: attenuation, convergence time, stabilityand robustness. To measure stability a subjectivemethod of classification was employed with gradesbeing stable, oscillating, unstable, very unstable, di-verging. A system configuration was classified withone grade based on the amount of runs it displayeda certain behaviour. Robustness was determined byinducing perturbations to the headset, specificallytaking off and putting on the headset. Attenuationwas the favoured measure to choose the best value,then it was convergence time, stability and for lastrobustness.

The resulting parameters of the optimization pro-cess are presented in Table 1. They were not neces-sarily the best combination of parameters since thestudy was incomplete, but presented a good balanceof attenuation, stability and speed while cancellingboth high level noises and low level noises.

This study proved valuable to understand theweight some parameters have on the performancemeasures used. The system revealed to be moreunstable for high sound pressure levels, with thiseffect being mitigated by using the leakage factor.However, it limits the output power of the system,thus reducing attenuation in the process. The low-est pre-amplifier gain generated the highest atten-uation. The convergence time increased with thefilter length. The convergence time decreased asthe step size increased. For the sampling frequency,stability and robustness was worse without multi-rate processing. With multi-rate processing, atten-uation was higher for 8 kHz but the stability androbustness was better with 2 kHz for some algo-

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rithms, namely the BMFxLMS algorithm.

Table 1: Parameters obtained from the experimen-tal parameter optimization.

µ λ Lw = Ls AVref

FxLMS fb 0,005 1 120 -BMFxLMS 0,005 1 55 -FxLMS ff 0,005 1 200 62,5

MMFxLMS 1 1 200 62,5

Tone frequency sweepIn this set of experiments the sinusoidal noise had

its frequency varied. The resulting attenuation wasnoted and other relevant measures of performanceobserved. Table 2 has a comparison of the attenu-ation results for each algorithm.

On average, the best attenuation is from the BM-FxLMS and the worse from the MMFxLMS. Thefeedback FxLMS algorithm was the least stable andthe MMFxLMS was the most stable. From theseresults, it can be concluded that the methods tocounter the modelling error effects were successfulin doing so.

Comparing to the literature results [9, 1], eventhough the system can achieve good attenuationlevels, superior to 30 dB, the results reported couldget over 40 dB of attenuation. This can be ex-plained by their methods employed to obtain theattenuation measures. Their attenuated noises wereacquired inside head simulators with high precisionmicrophones, whereas in this work the residual sig-nal, contaminated by background noise, was usedas the attenuated noise. The fixed controller head-set tested in [1] revealed to be inferior, however itis a very old model.

Narrowband noiseIn this procedure the primary noise used was an

industrial compressor, with narrowband spectrum.Some high power harmonics were observed for thetrials of each algorithm and their attenuation com-pared. In Table 3 the attenuation for the observedharmonics and the total attenuation are presented,for each algorithm.

The feedforward FxLMS had the best total atten-uation and on average of the observed harmonics.The spectrum of this algorithm attenuation can beseen in Figure 16. MMFxLMS had equally good av-erage attenuation for those harmonics, however theoverall performance was not very good. Althoughthe feedback FxLMS had the second best total at-tenuation, it was the algorithm with the worst sta-bility. The BMFxLMS improved on it but had theworst attenuation of harmonics. The feedforwardalgorithms had no stability issues.

The results of the prototypes reported in otherworks [11, 9] show that, although the present systemhas a worse total attenuation, the attenuation forharmonics higher than 100 Hz is comparable and forharmonics higher than 200 Hz is superior. In thoseworks commercial analogue headsets had their at-tenuation assessed. The system developed in thiswork had performance similar to that of the com-mercial headsets, therefore the results were good.

Figure 16: Power spectra of narrowband noise withand without ANC, for feedforward FxLMS.

Broadband NoiseBroadband noise was not cancelled by this sys-

tem. Figure 17 depicts the situation for the algo-rithm which had the best performance, the feedfor-ward FxLMS, since it did not increase the noiselevel in the system. For feedback systems thatwas expected, due to their inability to cancel thosenoise. The physical placement of the sensors forthe feedforward systems probably did not meet thecoherence and causality conditions.

Figure 17: Power spectra of broadband noise withand without ANC, for feedforward FxLMS.

5. ConclusionsThe active headset system, with both feedback andfeedforward configurations, showed satisfactory at-tenuation. Not only it reinforced the fact that feed-forward systems perform better than feedback sys-tems, but also demonstrated the superior attenu-ation of an adaptive controller compared to some

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Table 2: Attenuation of the algorithms with the tone frequency sweep. fb - algorithm for feedback system;ff - algorithm for feedforward system.

Frequency [Hz] FxLMS fb[dB] BMFxLMS[dB] FxLMS ff[dB] MMFxLMS[dB]60 21,62 23,73 19,62 16,62100 28,83 18,94 26,69 29,6200 28,27 28,45 20,52 29,72400 26,58 24,9 28,23 23,77500 26,35 38,93 32,37 25,03

Table 3: Attenuation of the algorithms with the narrowband noise. fb - algorithm for feedback system;ff - algorithm for feedforward system.

Frequency [Hz] FxLMS fb-Att[dB] BMFxLMS-Att[dB] FxLMS ff-Att[dB] MMFxLMS-Att[dB]82 11,06 3,65 20.45 23.41121 10,88 9,35 19.62 20.02

175,8 9,38 6,18 8.74 8207 18,35 8,12 18.63 15.13320 18,35 - 22.29 21.13

Total Attenuation 5.42 1.13 7.1 1.07

fixed controllers, seen in the consulted literature.However, it revealed instability issues related to themodelling error of the secondary path estimates, in-herent to the off-line modelling method.

The two approaches used to reduce the effectsof the phase error were successful mitigating them.The instability of the FxLMS algorithm was re-duced, however at the cost of reduced attenuationfor real noises. Still, the BMFxLMS was not com-pletely stable and it presented great lack of robust-ness. The MMFxLMS revealed to be robust to allperturbations but the take off/put on situation, itwas very stable when the numerical range of theCODEC was not exceeded by the overshoot inher-ent to it. This overshoot was the greatest drawbackof this algorithm, since, as stated, it also degradedits attenuation for real systems.

It should be noted that the tone frequency sweep,narrowband and broadband noises all used loudnoises, to maximize the attenuation achieved. How-ever, at these sound pressure levels, the stability ofthe system got worse.

The experimental results are acceptable since itcompares to, and sometimes it exceeds, the per-formance of the reported commercial analogue sys-tems, however it obtained inferior attenuation com-pared to recent results from other researchers. Thesystem presents stability issues, which can difficulta commercial application, thus they should be bet-ter studied.

It was made evident how important is a closerstudy of causality and coherence to achieve broad-band cancellation. For instance it would be usefulto measure the electrical delay of the CODEC andcompare to the acoustic delay of the system, to bet-ter study the causality of the system. Also a study

of the position of the reference microphone and itseffect on the performance of broadband noise can-cellation would be in order.

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