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IEEE TRANSACTIONS ON AUDIO, SPEECH, AND LANGUAGE PROCESSING, VOL. 20, NO. 9, NOVEMBER 2012 2549

Novel Acoustic Feedback Cancellation Approachesin Hearing Aid Applications Using Probe Noise

and Probe Noise EnhancementMeng Guo, Student Member, IEEE, Søren Holdt Jensen, Senior Member, IEEE, and Jesper Jensen

Abstract—Adaptive filters are widely used in acoustic feedbackcancellation systems and have evolved to be state-of-the-art. Onemajor challenge remaining is that the adaptive filter estimates arebiased due to the nonzero correlation between the loudspeakersignals and the signals entering the audio system. In many cases,this bias problem causes the cancellation system to fail. The tradi-tional probe noise approach, where a noise signal is added to theloudspeaker signal can, in theory, prevent the bias. However, inpractice, the probe noise level must often be so high that the noiseis clearly audible and annoying; this makes the traditional probenoise approach less useful in practical applications. In this work,we explain theoretically the decreased convergence rate whenusing low-level probe noise in the traditional approach, before wepropose and study analytically two new probe noise approachesutilizing a combination of specifically designed probe noise signalsand probe noise enhancement. Despite using low-level and in-audible probe noise signals, both approaches significantly improvethe convergence behavior of the cancellation system compared tothe traditional probe noise approach. This makes the proposedapproaches much more attractive in practical applications. Wedemonstrate this through a simulation experiment with audio sig-nals in a hearing aid acoustic feedback cancellation system, wherethe convergence rate is improved by as much as a factor of 10.

Index Terms—Acoustic feedback cancellation, adaptive filters,hearing aids, probe noise, probe noise enhancement.

I. INTRODUCTION

A COUSTIC feedback problems may occur in audio sys-tems when the microphone picks up part of the acoustic

output signal from the loudspeaker. This problem often causessignificant performance degradations in applications such aspublic address systems and hearing aids. In the worst-case,the audio system becomes unstable and howling occurs. Manysolutions have been proposed for reducing the effect of acousticfeedback, see e.g. [1], [2] and the references therein. A widely

Manuscript received March 14, 2012; revised June 06, 2012; accepted June08, 2012. Date of publication June 26, 2012; date of current version August24, 2012. The associate editor coordinating the review of this manuscript andapproving it for publication was Prof. Sharon Gannot.

M. Guo is with the Department of Electronic Systems, Aalborg University,DK-9220 Aalborg, Denmark, and also with Oticon A/S, DK-2765 Smørum,Denmark (e-mail: [email protected]).

S. H. Jensen is with the Department of Electronic Systems, Aalborg Univer-sity, DK-9220 Aalborg, Denmark (e-mail: [email protected]).

J. Jensen is with Oticon A/S, DK-2765 Smørum, Denmark (e-mail:[email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TASL.2012.2206025

Fig. 1. A traditional acoustic feedback cancellation approach in a multiple-microphone and single-loudspeaker system.

used and probably the best solution to date is to use adaptivefilters in a system identification configuration [3].

Fig. 1 shows a general acoustic feedback cancellation (AFC)approach using adaptive filters in a multiple-microphone andsingle-loudspeaker (MMSL) audio system, where AFC is car-ried out using the adaptive filters to compensate for thetrue acoustic feedback paths , where is the discrete-timeindex, , and is the number of microphones. Theestimation of the true feedback paths by means of adap-tive filters is based on the loudspeaker signal andthe error signals and can be performed using e.g. leastmean square (LMS), normalized least mean square (NLMS),and recursive least squares (RLS) algorithms [3], [4]. The in-coming signals to the microphones of the MMSL system aredenoted by . Often, multiple-microphone audio systemsare equipped with a beamforming algorithm to perform spa-tial filtering of the incoming signals. The beamformer filtersprocess the error signals to form a spatially filtered beam-former output signal , which is further modified by the for-ward path to produce the loudspeaker signal . Moredetails on Fig. 1 are given in Section II-A.

The adaptive filter approximates the acoustic feedbackpath . Although AFC using adaptive filters is one of themost applied methods to compensate for the feedback problem,one of the major problems remaining is that the estimatesbecome biased, i.e. , where denotes thestatistical expectation operator, whenever the loudspeaker signal

and the incoming signals are correlated [5]. Thisis generally unavoidable in closed-loop systems as e.g. shownin Fig. 1, because the loudspeaker signal is a processedand delayed version of the incoming signals . The biasedestimation of may lead to a poor feedback cancellationand in the worst-case causes the cancellation system to fail.

Different techniques have been proposed to prevent or reducethe biased estimation problem. Nonlinear processing methods

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2550 IEEE TRANSACTIONS ON AUDIO, SPEECH, AND LANGUAGE PROCESSING, VOL. 20, NO. 9, NOVEMBER 2012

Fig. 2. A traditional probe noise based acoustic feedback cancellation approachin a multiple-microphone and single-loudspeaker system.

[1] add an ideally inaudible, nonlinearly distorted version ofloudspeaker signal to to decorrelate it from the in-coming signals . Typically, a half-wave rectifier is used tointroduce the distortion. The frequency transposition methods[6], [7] introduce a modification in the forward path , by e.g.shifting the frequency components from the incoming signals

to other frequencies. Thus, it decorrelates the loudspeakersignal and the incoming signals and is thereby ca-pable of reducing the bias problem. The prediction error method[8], [9] utilizes prefilters applied to the signals entering the adap-tive filter estimation; the prefilters are used to approximatelywhiten the incoming signal components in these signals andthereby compensate for the biased estimation.

In this work, we focus on the probe noise approach. Fig. 2shows a traditional probe noise approach in an MMSL system.The probe noise signal is added to the original loudspeakersignal to facilitate unbiased estimation of the true feedbackpaths . In contrast to the traditional AFC approach shownin Fig. 1, the adaptive filters are estimated based on theprobe noise signal and the error signals , and un-biased estimation is guaranteed since is uncorrelated with

and by construction. More details on Fig. 2 are givenin Section II-B.

Adaptive filter estimation based on probe noise can be car-ried out in different ways. In [10], the adaptive filter estimatesare only updated when the system is detected to be close to in-stability; in this case, the original loudspeaker signal ismuted, and only the probe noise signal is presented as theloudspeaker signal to perform the estimation. In [11], an attemptis made to reduce the audible artifacts introduced by a high-levelprobe noise signal; specifically, probe noise insertion and adap-tive filter estimation is only performed during quiet intervals.In both cases, a non-continuous adaptation is carried out, andthe cancellation performance is highly dependent on the deci-sions made by the stability and quiet-interval detectors, respec-tively. For input signals with few quiet passages, e.g. musicalsignals, these systems can not update their feedback path esti-mate and are therefore sensitive to feedback path changes. Inother probe noise approaches [12], [13], an estimate ofthe loudspeaker signal is created by using a probe noisesignal in an open-loop system identification configuration, andthe adaptive filter estimation relies on this estimated signalinstead of ; is ideally uncorrelated with , andan unbiased estimation can thereby be obtained. However, the

drawback is that a loud and clearly audible probe noise signal isrequired.

In principle, all these probe noise approaches can prevent thebias problem and improve the cancellation performance. In [14],it was shown that the traditional probe noise approach is ca-pable of providing similar or even better performance than otherstate-of-the-art AFC approaches, but only if the level of probenoise is powerful enough compared to the original loud-speaker signal , see also [13], [15]. On the other hand, whenthe probe noise level is adjusted to be inaudible, the convergencerate of the adaptive algorithm is often highly decreased (whilemaintaining the steady-state error), which limits the practicaluse of the probe noise approach in an AFC system. In [16] itwas shown theoretically that when using the traditional probenoise approach with inaudible probe noise signals, the conver-gence rate of the adaptive system is decreased, by as much asa factor 30 in practice. Based on [16], a theoretical frame workwas proposed in [17] for an improved probe noise approach,which is capable of significantly increasing the convergence ratewithout compromising the steady-state error at a given probenoise level. In this paper, we present a comprehensive theoret-ical analysis of the improved approach in [17] and discuss someimportant practical aspects of its application in real situations.Within the same theoretical framework, we present a further im-proved probe noise approach, where the convergence rate is in-creased by up to a factor 2 compared to [17] with only minimaladditional calculations.

The improvements by the proposed probe noise approachesare obtained by processing the signals entering the adaptive al-gorithms, such that the disturbance from the incoming signals

is reduced. Additionally, both improved approaches uti-lize a simple spectral masking model to generate a probe noisesignal , which is inaudible in the presence of the orig-inal loudspeaker signal . This provides a resulting loud-speaker signal that is perceived essentially identically tothe original loudspeaker signal . This probe noise genera-tion method was introduced for AFC applications in [18].

For both proposed approaches, we derive analytical expres-sions for their system behavior; we compare them to a tradi-tional AFC system without probe noise [19], and a traditionalprobe noise based AFC system [16]. Furthermore, we demon-strate the improvements in simulation experiments using audiosignals and practical parameter settings in a realistic hearing aidAFC system.

In this work, column vectors and matrices are emphasizedusing lower and upper letters in bold, respectively. Transposi-tion, Hermitian transposition and complex conjugation are de-noted by the superscripts , and , respectively.

The rest of this paper is organized as follows. In Section II,we introduce different MMSL systems using the traditionalAFC approach, traditional probe noise approach and the twoproposed probe noise approaches. In Section III, we deriveanalytic expressions for the system behavior in terms of con-vergence rate and steady-state behavior to explain analyticallythe improvements obtained using the proposed approaches. InSection IV, we perform simulation experiments, using audiosignals, to compare the proposed probe noise approaches to

GUO et al.: NOVEL ACOUSTIC FEEDBACK CANCELLATION APPROACHES IN HEARING AID APPLICATIONS 2551

the traditional probe noise approach and the traditional AFCapproach. Finally, we conclude this work in Section V.

II. SYSTEM OVERVIEW

In this section, we introduce MMSL systems using the fourdifferent AFC approaches, which are considered in this work: 1)The traditional AFC approach (T-AFC). 2) A traditional probenoise approach (T-PN). 3) The proposed probe noise approach I(PN-I) in [17]. 4) The proposed probe noise approach II (PN-II).

For convenience, we express all signals as discrete-time sig-nals, although in practice the signals entering the microphonesand leaving the loudspeaker are continuous-time signals.

A. Traditional AFC Approach (T-AFC)

Fig. 1 shows the MMSL system using the T-AFC ap-proach. The th true acoustic feedback path

is assumed to be a finite im-pulse response (FIR) of order . The frequency responseof is expressed by the discrete Fourier transform (DFT)

, where is the discretenormalized frequency.

There are different ways to model feedback path variationsover time, see e.g. [20]. In this work, we use a simple randomwalk model given byfor the th feedback path, where is a samplefrom an independent zero-mean Gaussian stochastic sequencewith cross-covariance . Thus,in the time domain, the feedback path variation vector is

(1)

The adaptively estimated feedback path of orderis expressed by , and theestimation error vector is

(2)

with a frequency response .In this work, we denote the lengths of both and

with . We assume that has a sufficient length , in prin-ciple . Thus, the effective length of could beshorter than , e.g. in the case when is zero-padded tothe length .

The signal vector for the loudspeaker signal isdefined as , whereas theth microphone signal is modeled as1

(3)

and the th feedback compensated error signal is given by

(4)

1At least one delay element is needed in closed-loop systems to avoid analgebraic loop. As in [21], we chose to model this delay in � by using thetime index �� for notational convenience, since it then would appear to havethe same time index as its parallel-structured acoustic feedback path estimate�� . This notation of time indexing does not affect the result.

The adaptive estimation of can e.g. be performed usingthe LMS algorithm [3] with the step size and the updaterule

(5)

although many more options exist, see e.g. [3], [4].In the MMSL system shown in Fig. 1, spatial filtering is

carried out using a simple linear beamformer [22] applied tothe error signals . In this work, the beamformer filters

are considered fixed because they are often slowly varyingcompared to AFC systems; they are represented by FIR filters

of order , with afrequency response . The outputsignal of the beamformer is therefore

.Although it is possible to reverse the order of the beamformer

and the acoustic feedback cancellation system, we only focus onthe case where the cancellation is performed prior to the beam-former as given in Fig. 1. This setup requires more computa-tional power due to multiple cancellation systems, but the beam-former would not affect the cancellation process negatively asdemonstrated in [23].

The forward path represents the process of convertingto the loudspeaker signal . Generally, the forward pathconsists of an amplification and a processing delay for

closed-loop audio systems. The impulse response of the forwardpath is denoted by with afrequency response , and theloudspeaker signal is obtained as

.

B. Traditional Probe Noise Approach (T-PN)

Fig. 2 shows the MMSL system using the T-PN approach.The significant difference compared to the T-AFC systemin Fig. 1 is that a probe noise signal is added to theoriginal loudspeaker signal , and is used directlyfor updating . The probe noise signal vector is definedas . The resulting loud-speaker signal is with a signal vector

, where

(6)

The th microphone signal is given by

(7)

and the th error signal is expressed by

(8)

The goal of the probe noise is to ensure an unbiased es-timation of , because the probe noise signal is con-structed to be uncorrelated with both the incoming signalsand the original loudspeaker signal , see e.g. [2], [5] fordetails. The probe noise is generated, using a known spectralshaping filter , as


Fig. 3. The improved probe noise acoustic feedback cancellation approach ina multiple-microphone and single-loudspeaker system. The traditional probenoise approach is obtained by setting the filters � �� .

, where is a zero-meanGaussian stochastic sequence with unit variance. In this work,we generate a probe noise signal which is ideally inaudiblein the presence of by adaptively updating basedon the spectral properties of ; details on this are given inSection IV-B-3. Generally speaking, the goal of this is to maxi-mize the power of the probe noise such that it is just not audible.

The unbiased estimation of is driven by the probe noisesignal and can e.g. be obtained using an update rule similarto (5), that is

(9)

C. Proposed Probe Noise Approach I (PN-I)

Fig. 3 shows the PN-I approach presented in [17]. The differ-ence from the T-PN approach in Fig. 2 is the introduction of theso-called enhancement filters applied to the error signals

.Ideally, in the adaptive filter estimation in a system identi-

fication configuration, the error signal entering the estimationblock of is . In practice, however,the error signal contains also signal components such as

and , which are disturbing the esti-mation of . The goal of the enhancement filters is toreduce the disturbing signal power, without changing the probenoise power for the estimation of at the same time [17].As we will explain in more details in Section III, the higher thepower ratio between the probe noise and the disturbing signals,the faster convergence can be achieved given a fixed steady-stateerror in the adaptive cancellation system. As improvesthe probe noise to disturbing signal ratio, an increased con-vergence rate can be obtained compared to the T-PN approachwithout compromising the steady-state behavior in the cancel-lation system.

The increased probe noise to disturbing signal ratio is ob-tained by a specific design procedure of the enhancement filter

, which is closely related to the probe noise shaping filterlength and the feedback path length . In this work, we as-sume that the same enhancement filter is applied across micro-phone channels, i.e. . This is not strictly necessary,but gives a simple result. Furthermore, for audio systems withclosely placed microphones such as hearing aids, this is a rea-sonable simplification. Furthermore, the enhancement filter is

presented by an order FIR. Very importantly, the design of is constrained such

that its frequency response is expressed by

(10)

and the value is chosen as

(11)

Thus, the structure of the enhancement filter is, and it is estimated as

(12)

Thus, it is clear that is simply the mean square error (MSE)prediction error filter [3]. Furthermore, for a large value of in(11), it becomes a long-term prediction error filter [24]. We willexplain the reason for these choices in Section III.

The filtered error signal is expressed by

(13)

and the unbiased feedback path estimation is carried out bybasing the estimation of on the probe noise signaland filtered error signal , e.g. using the update rule

(14)

which is similar in structure to the LMS update rule used in (5).

D. Proposed Probe Noise Approach II (PN-II)

It is possible to further improve the PN-I approach. This isdone by applying copies of the enhancement filter to theprobe noise signal to form as shown in Fig. 4, inwhich the general terminology is used, although we as-sume for simplicity. As we will show throughthe theoretical analysis in Section III, these copies of onthe probe noise signal lead to even higher probe noise todisturbing signals ratio than the PN-I approach shown in Fig. 3,by increasing the effective probe noise power for the estimationof . Thus, a further increment of the convergence can beobtained in this cancellation system.

Due to the assumption of , the filtered probenoise is obtained as

(15)

The probe noise signal vector is defined as, and an unbiased feedback path

estimation can be carried out e.g. using the update rule

(16)


Fig. 4. The further improved probe noise acoustic feedback cancellation ap-proaches in a multiple-microphone and single-loudspeaker system. The differ-ence is that the copies of � �� are applied on the probe noise signal �� toform �� which are used in the estimation of � ��.

III. THEORETICAL ANALYSIS

In this section, we derive analytic expressions to describesystem behavior in terms of convergence rate and steady-stateerror, as a function of time and frequency, based on the exampleupdate rules in (5), (9), (14) and (16). The derived expressionsexplain analytically the differences between all four consideredAFC approaches. Later in this section, simple simulations areperformed to verify the derived expressions.

A. Review of Power Transfer Function

The theoretical analysis of the system behavior is based ona recently introduced frequency domain design and evaluationcriterion for adaptive systems, the power transfer function (PTF)[19], which describes the expected magnitude-squared transferfunction from point A to B in Figs. 1–4. More specifically, thePTF is expressed by

(17)

and it represents the unknown part of the expected magni-tude-squared open-loop transfer function,

. If , system stabilityis guaranteed [25]. Hence, provides important infor-mation of system behavior. The PTF can generally not becomputed directly because the true acoustic feedback paths

and thereby are un-known. However, as shown in [19], it is possible to obtain anaccurate approximation of . This approximationis expressed by a first-order difference equation in .Based on this, it is possible to determine the convergence rateand steady-state behavior for the system under concern.

As in [19], we let and via(17) the PTF approximation can be shown to be

(18)

In the following, we briefly review the PTF approximationfor the MMSL system using the T-AFC approach

[19], and the T-PN approach [16]. Then, we derive the PTFapproximation for the PN-I and PN-II approaches.The derivations and comparisons provide a theoretical expla-nation of the motivation and improvements by the proposedapproaches. For simplicity, the derivation is carried out inan open-loop configuration by omitting in the MMSLsystems. It can be shown that this has only minor effects onthe practical use of the derived results for closed-loop AFCapproaches in general [26], and it has no influences on thetechnical explanations provided in this section. Finally, we as-sume for simplicity the incoming signals are zero-meanstationary stochastic signals in the analysis.

B. Analytic Expressions for System Behavior

1) Some Definitions: To ease the derivation, we as-sume and divide it further into the parts

and,

such that

(19)

The frequency responses of and are and, respectively.

Furthermore, we define the Toeplitz-structured filtering ma-trix , with the dimension , as

. . ....

. . ....

. . .

. . ....

. . .. . .

.... . .

(20)where , 1, so that we get the matrices and . Fur-thermore, we define

(21)

Finally, we define the vectorsand .

2) Traditional AFC Approach (T-AFC): In [19], the PTF ap-proximation for the MMSL system shown in Fig. 1, using theupdate rule in (5), was derived as

(22)

where denotes the power spectrum density (PSD) of theloudspeaker signal , and denotes the auto/cross


PSDs of the incoming signals and . Eq. (22) was de-rived under the assumptions of sufficiently small step sizeand large model order parameter , in principle, and

. In (22), the last term is slightly modified compared tothe result in [19], since the additional simplifying assumptionof was applied in [19].

3) Traditional Probe Noise Approach (T-PN): In [16], thePTF approximation for the MMSL system using the T-PN ap-proach shown in Fig. 2 and the update rule in (9) was derived.Under the same assumptions of and as for the T-AFCapproach, it can be shown that

(23)

where denotes the PSD of the probe noise signal .In (23), the last term is again slightly modified compared tothe result in [16] with the additional simplifying assumption of

.4) Proposed Probe Noise Approach I (PN-I): In [17], we pro-

vided the final PTF expression for the PN-I approach inFig. 3 without detailed derivations. This section provides moredetails towards this result. The methodology used for the deriva-tion is similar to the one presented in [26]. However, in con-trast to [26], we consider the original loudspeaker signalas a disturbing signal for the estimation of . Additionally,we need to deal with the effects of enhancement filter ondifferent signals and ensure that the estimation of is stillunbiased. In the following, we derive for the PN-I ap-proach with emphasis on this consideration.

Define the matricesand . Then, using (6)–(8)and (13), the example update rule for given by (14), forthe PN-I approach shown in Fig. 3, can be expressed as

(24)

It can be shown (see Appendix A) when the enhancement filterfulfills the important constraint in (11), then

unbiased estimation of is ensured, i.e. .In order to derive the PTF expression , we use (24),

(19) and (1) to express the estimation error vector defined in (2)as

(25)

The approximation of the estimation error (auto-) covariancematrix is computed using (25),under the assumption of sufficiently small , in principle

, and by neglecting the second-order terms involvingdue to the presence of their first-order versions. In ad-

dition, we consider and as deterministic signals

in deriving (26). As argued in [21] and demonstrated in oursimulation experiments, the resulting expression is valid evenfor the case where and are in fact realizations ofstochastic processes. The approximation of becomes

(26)

where the correlation matrix of the th and th feedback pathvariations is defined as .

Eq. (26) can be simplified. Recall that is uncorre-lated with , thereby .Furthermore, since by construction, see(11), it can be shown that(see Appendix B). Using the direct-averaging method [27]to replace the matrix with its sampleaverage ,the matrix with its sample average

, andthe matrix with its sample average

, the ap-proximation in (26) can be simplified to

(27)

We now bring the time domain expression in (27) to the fre-quency domain to simplify it further. Recall that, asymptoti-cally as , the DFT matrix diagonalizes anyToeplitz matrix [28]. Using this, we can show that areobtained as the diagonal values of the matrix ex-pressed by

(28)

Details on this derivation can be found in [26]. Inserting (28) in(18), the PTF approximation is finally obtained as

(29)


5) Proposed Probe Noise Approach II (PN-II): In the deriva-tion of the PN-II approach, extra attention must be paid to thecopies of the enhancement filter filtering the probe noise signal

; otherwise, the same procedure is applied as for the PN-Iapproach.

Using (6)–(8), (13) and (15), the estimate of given by(16) can be written as

(30)

Similarly to the PN-I approach, it can be shown that an unbiasedestimation of can be obtained as long as the constraint onthe enhancement filter in (11) is obeyed.

Using (30), (19) and (1), the estimation error vector definedin (2) can also be expressed by

(31)

The approximation of the estimation error (auto-) covariancematrix is again computed, under the assumption of suf-ficiently small , and by neglecting the second-order termsinvolving in the presence of their first-order versions, as

(32)

Considering that, and using the direct-averaging method to

further rewrite as ,then the matrix

is identical to as , be-cause and are both signal vectors containing

, but with different dimensions. Similarly, we rewriteas , where

. Theapproximation can therefore be simplified to

(33)

Using similar considerations as in Appendix B, the matrixcan be expressed by

(34)

Inserting (34) in (33), and again using the DFT matrix todiagonalize in (33), it can be shown thatare obtained as the diagonal elements of the resulting matrix

, as

(35)

Finally, inserting (35) in (18), the resulting PTF is ex-pressed by

(36)

C. Discussion

1) Resulting Expressions for all Approaches: Eqs. (22), (23),(29) and (36) are first-order difference equations inand determine the behavior of the corresponding systems. Inparticular, we determine the convergence rate describing thedecay rate of per sample period, and the steady-statebehavior which is the sum of steady-state andtracking errors upon convergence of . The steady-stateerror describes the lowest possible steady-state value of ,whereas the tracking error is the additional error to that dueto the variations in the acoustic feedback paths. The resultingexpressions are given in Table I, for ease of a comparisonbetween the different approaches.

2) T-PN vs. T-AFC: It is seen from Table I that the only dif-ference between the T-AFC approach and the T-PN approach isthat for the convergence rate and the tracking error, is re-placed by . Because must generally be much lowerthan to ensure the added probe noise is inaudible, the con-vergence rate in T-PN is reduced by the factor ,which is typically as large as 30, and the tracking error is in-creased by the same amount.

3) PN-I vs. T-PN: The only modification introduced by thePN-I approach is the scaling of the steady-state error by the


TABLE ISYSTEM BEHAVIOR IN TERMS OF CONVERGENCE RATE (CR), STEADY-STATE ERROR (SSE) AND TRACKING ERROR (TE) AT FREQUENCY �, FOR THE TRADITIONAL

AFC APPROACH (T-AFC), TRADITIONAL PROBE NOISE AFC APPROACH (T-PN), PROPOSED PROBE NOISE APPROACH I (PN-I) AND THE PROPOSED PROBE NOISE

APPROACH II (PN-II). FOR READING CONVENIENCE, WE INTRODUCE � � � �� AND � � � ��

factor of compared to the T-PN approach. Thus, de-pending on , the PN-I approach has the capability of re-ducing the steady-state error compared to the T-PN approach,while maintaining the convergence rate and tracking error. Thisis obtained for , i.e. in frequency regions wherethe enhancement filter can (partly) predict based onits past samples, via . Recallthat the enhancement filter is found as the MSE long-termprediction error filter in (12), and can be con-sidered as the direct and prediction part of the filtered errorsignal . Thus, is able to (partly) pre-dict/remove the disturbing signals, e.g. the incoming signals

, for the estimation of , as long as the autocorrela-tion function has nonzero lags for

. This typically occurs for tonal signals with clear spec-tral peaks, where provides a precise estimate of ,so that and . Thus, a reduc-tion in steady-state error is expected using the PN-I approach,particularly in frequency regions of with distinct spectralpeaks.

On the other hand, as shown in Appendices A and B, due tothe structure of the enhancement filter , in particular, the con-straint of given in (11), does not have any influence on theprobe noise signal either in the expected valuenor in the covariance calculation of . Thus, the enhance-ment filter can be considered statistically transparent for theprobe noise signal in the estimation of .

To summarize, in the PN-I approach, the different character-istics of the specifically designed enhancement filter on theprobe noise signal with limited correlation time and disturbingsignals lead to a reduced steady-state error without sacrificingthe convergence rate and tracking error. The degree of reductionin steady-state error depends on the capability of the enhance-ment filter to predict/remove the disturbing signals. Typically,a better prediction and thereby higher reduction in steady-stateerror can be obtained for tonal signals. Furthermore, it is pos-sible to apply an increased step size to obtain a higherconvergence rate and lower tracking error in the PN-I approach,while still obtaining an unchanged steady-state error as in theT-PN approach. In this way, part of the drop in convergence rateassociated with T-PN approach can be regained.

4) PN-II vs. PN-I: The idea behind the PN-II approach issimilar to the PN-I approach, i.e. utilizing the long-term predic-tion characteristic of the enhancement filter . The copies ofto generate the filtered probe noise signalmakes it possible to achieve further improvements, where

and can be considered as thedirect and prediction part of the signal , however, and

are uncorrelated due to the constraint on . The introduc-tion of the extra enhancement filters applied to means thatinstead of considering the terms involving

in (26), whereas shown in Appendix A, we are

now considering the terms involvingin (32) in the calculation of in the PN-II approach, andwe get the additional contribution in (34).This corresponds to utilizing both the direct parts of signals

and , and the prediction parts and ofthe filtered signals and for the estimation of .

In this way, in contrast to the PN-I approach, wherethe expected disturbing signal power is reducedand the expected probe noise power can beconsidered unchanged, the expected probe noise power

for the estimation algo-rithm and thereby the probe noise to disturbing signal ratiois further increased in the PN-II approach. As the result, theconvergence rate and tracking error are increased by the factorof , with at the frequency wherethe enhancement filter is able to make a reasonable predictionof from its past samples .Hence, in the PN-II approach, the convergence rate can befurther increased by the factor , andthe tracking error is reduced by the same amount, while main-taining the steady-state error as in the PN-I approach.

Although the proposed probe noise approaches PN-I shownin Fig. 3 and especially PN-II shown in Fig. 4 are somewhat sim-ilar in structure to the decorrelating prefilter method [9], whereprefilters are applied to the loudspeaker and error signals in asimilar way to the enhancement filters, their goal and procedureare very different. The goal of the prefilters in [9] is to decor-relate the incoming signals and the loudspeaker signal

, whereas the goal of the enhancement filters is to increasethe probe noise to disturbing signal ratio. Furthermore, the pro-posed approaches differ from the decorrelating prefilter methodby using long-term prediction error filters as the enhancementfilters.

D. Verification of Analysis Results

To complete the analytical analysis and discussion, we per-form simple simulation experiments to verify the derived PTFexpressions in (23), (29) and (36), for the different probe noise


approaches shown in Figs. 2–4, respectively, and to visuallydemonstrate the improvements.

The simulations are performed in a closed-loop AFC systemin a hearing aid setup with microphones, using asampling frequency kHz. The feedback pathsand are measured from a behind-the-ear hearing aid withan order of about 50. Because the impulse responsesare known, we can compute the true PTF accordingto (17) to verify the derived expressions for . We com-pute as the average across simulation runs,

i.e. , whereis the result of the th simulation run.

A simple beamformer is used, . The forwardpath has a delay of 120 samples modeling a hearing aidprocessing delay of 6 ms, and it has a fixed amplification of ap-proximately 29 dB so that the most critical frequency for systemstability can be found at approximately 2.5 kHz, where the mag-nitude value of the open-loop transfer function is 1 dB and thephase is 0 rad.

The adaptive filters have a length of and areinitialized as . The true feedback paths arefixed during the first part of the simulation, whereas randomwalk variations with variances and

are added during the last 15 s. Three different sim-ulation experiments are carried out using the T-PN, PN-I and thePN-II approaches. The step size values are respectively chosento be , and for all three experiments, in order toobtain same steady-state errors but different convergence ratesand tracking errors.

In each simulation run, new realizations of standard Gaussianstochastic sequences are drawn; the incoming signals andthe probe noise signal are obtained as these sequences fil-tered by the inverse of the enhancement filter and probe noiseshaping filter , respectively. Both filters are known and fixedin this simulation experiment, because the goal of this exper-iment is to verify the derived expressions; we postpone sim-ulation of the more practical situation where these filters aretime-varying to the next section. The shaping filter with alength is created by first computing as the PSD

scaled by the forward path amplification of 29 dB, andthen the PSD is computed as a scaled ver-sion of . Finally, the filter is designed using the fre-quency sampling method. The power ratio between the signals

and is thereby 12 dB; clearly, the probe noise willgenerally be audible in this case. In the next section, we demon-strate system performance when the noise is created to be in-audible. The enhancement filter has a length of witha value of to fulfill the requirement of ,and its magnitude response has a sharp notch at 2.5 kHz.

Fig. 5 shows the simulation results verifying the PTF predic-tion values, at the most critical frequency , where

, corresponding to 2.5 kHz. In all cases, the values predictedfrom the derived expressions are successfully verified by thesimulation results. Furthermore, the desired steady-state errorof approximately 52 dB is obtained for all three approaches,but very clearly, the convergence rates and the tracking errorsare completely different, as expected. Due to the difference in

Fig. 5. Verification at the frequency of 2.5 kHz. (a) The traditional probe noiseapproach (T-PN). (b) The proposed probe noise approach I (PN-I). (c) The pro-posed probe noise approach II (PN-II).

step sizes by a factor of 8, the convergence rate is increased andthe tracking error is reduced by the same amount for the PN-Iapproach compared to the T-PN approach. Furthermore, it isseen that by using an identical step size in the PN-II approach,the convergence rate and tracking error is further modified by afactor of approximately 1.8 due to the extra enhancement filtersapplied on the probe noise signal.

IV. DEMONSTRATION IN A PRACTICAL APPLICATION

In this section, we perform simulations using audio signals ina hearing aid AFC system with microphones. The goalof the simulations is to show the improvements by the proposedPN-I and PN-II approaches compared to the T-PN approach in apractical situation, where enhancement filters are time-varyingand estimated based on available signals only, the probe noisesignal is generated using a spectral masking model tobe inaudible in the presence of the original loudspeaker signal

, and the feedback paths exhibit quick changes, e.g.corresponding to a telephone-to-ear situation, which is knownto be a difficult scenario for hearing aid AFC systems. We showthat whereas the T-AFC and the T-PN approaches fail to cancelthe acoustic feedback, the proposed PN-I and PN-II approachesare efficient in doing so.

A. Acoustic Environment

The simulations are carried out using a sampling frequencyof kHz. In the following, we provide information ofthe true feedback paths and the audio signal used to generatethe incoming signals in the simulations.

1) Acoustic Feedback Paths: The true acoustic feedbackpaths denoted as in Figs. 1–4 are obtained by measure-ments from a behind-the-ear hearing aid while worn by a test


Fig. 6. The measured acoustic feedback paths without and with a telephoneclosely placed to the hearing aid. (a) Impulse response. (b) Magnitude response.(c) Phase response.

person. The hearing aid has two omnidirectional microphonesand a loudspeaker. We divide the entire simulation into twodifferent periods. In both periods, the true feedback paths

are stationary. At the transition between the periods, wechange the feedback paths momentarily to simulate a situationwhere the hearing aid user makes a phone call and places atelephone close to the ear and thereby the hearing aid. Thischange of feedback paths is usually very challenging for AFCsystems, because sound reflected on the phone/hand back to themicrophones increases the feedback path magnitude responseby as much as 16 dB [29], almost momentarily, and the AFCsystem must adapt to the new acoustic feedback paths veryquickly to prevent the system from becoming unstable.

The feedback paths used before the transition were measuredwithout any obstacles in the close proximity of the hearing aid,whereas the feedback paths used after the transition were mea-sured when a telephone is closely placed to the ear (less than1 cm). Fig. 6 shows the impulse and frequency responses of thetrue feedback paths. It is clearly seen that the telephone-to-eartransition in this example increases the magnitude response inthe order of 5–10 dB for most frequencies.

2) Incoming Signals: The bias problem in general AFC sys-tems typically occurs for tonal signals due to their long cor-relation time. Although the traditional probe noise approachescan be used to avoid the bias problem in this situation, otherside effects such as decreased convergence rate would appear.Therefore, in order to make the demonstration most convincing,we choose an audio signal which has some significant spectralpeaks. In particular, we choose an audio signal with a very dom-inating flute sound around 2.5 kHz as shown in the spectrogramin Fig. 7.

The audio signal shown in Fig. 7 is used as a basis for the in-coming signals and . For a longer simulation, this

Fig. 7. The spectrogram of an audio signal used for generating the incomingsignals. The window size is 512 samples with 50% overlap, and a Hanningwindow is applied. Furthermore, for reading convenience, we limit the fre-quency axis to 0–6 kHz, because most frequency content of the signal arefound in this range.

audio signal is repeated. In order to perform beamforming, thetwo hearing aid microphones are typically aligned in the hori-zontal plane and in the same direction as the face of the hearingaid user; the distance between them is often about 15 mm. Inthe following simulations, we simply apply a delay to model thedistance between the microphones. The audio signal of Fig. 7 isused as the incoming signal , whereas the incoming signal

is generated by delaying by one sample. This sim-ulates the source signal coming from the frontal direction, witha distance between the two microphones of about 17 mm.

B. System Setup

1) Forward Path and Beamformer: Similar to the simulationexperiment in Section III-D, we apply a simple beamformer bysetting . Furthermore, a hearing aid input-to-output processing delay is typically around 4–8 ms [30]; in thissimulation experiment, we model this as a pure delay of 120samples corresponding to 6 ms in the forward path .

In contrast to the experiment in Section III-D, the forwardpath in the present experiment provides a time-varyingamplification using a single-channel fullband compressor [31].The amplification over time is computed as a function of thepower level of the signal . The compressor provides, forall frequencies, an amplification of 29 dB when the estimatedpower level is below a certain point, and the amplification is re-duced by the excess amount of the estimated power level abovethis point. With the chosen compressor settings and the acousticfeedback paths, the most critical frequency is found at about2.5 kHz, where the magnitude of the open-loop transfer functionis about 1 dB and the phase 0 rad at the beginning of the sim-ulation; it means that the system initially is close to instabilitywithout an AFC system. At the feedback path transition, theworst-case magnitude value of the open-loop transfer functionincreases momentarily to about 4.5 dB without an AFC system,and the system would certainly become unstable without a prop-erly working AFC system.

2) AFC Using Delayless Subband Adaptive Filters: In prac-tical applications, implementing AFC using a subband structureis often preferred for obtaining higher convergence rate and areduction in computational complexity [32]. In this work, weapply a delayless subband adaptive filter (SAF) in a closed-loopstructure [33], [34] to obtain in the estimation blocksshown in Figs. 1–4.

The length of the fullband filter is chosen to be .The subband NLMS step size for the PN-I and PN-II approachesis chosen as for all subbands except the lowest one,where the step size is set to 0. Thus, AFC is not performed below


TABLE IITHE OUTPUT SCORES GIVEN BY THE APPLIED PESQ AND PEAQ MODELS

TABLE IIISEVERAL TEST SIGNALS WITH INSERTED PROBE NOISE ARE OBJECTIVELY

EVALUATED USING PESQ OR PEAQ. THE PROBE NOISES ARE EITHER

PERCEPTUALLY GENERATED PROBE NOISE (PGPB) OR WHITE NOISE

AT THE SNR 60 dB (WN60), 40 dB (WN40) AND 20 dB (WN20)

approximately 500 Hz, because there is generally no feedbackproblem at the lowest frequencies in hearing aid applications, ase.g. seen in Fig. 6(b). For the T-PN and T-AFC approaches, thestep size is decreased by a factor of 6, so that the steady-stateerror is approximately the same for all approaches.

3) Probe Noise Generation: The probe noise signalshould be generated with the highest possible signal power ateach frequency while being inaudible in the presence of theoriginal loudspeaker signal . This can e.g. be achieved byusing perceptual audio coding techniques, see e.g. [35] and thereferences therein, based on the masking effects of the humanauditory system [36]. In this work, we generate the probe noisesignal using a spectral masking model based on [37]. For agiven loudspeaker signal , the model estimates a maskingthreshold ; ideally, additive and uncorrelated noiseshaped according to this threshold would be inaudible in thepresence of .

The shaping filter with length is createdusing the frequency sampling filter design method, based on

. In order to verify that the generated probe noiseis essentially inaudible in the presence of , we performedcontrol measurements, based on the perceptual evaluation ofspeech quality (PESQ) and perceptual evaluation of audioquality (PEAQ) models, described in [38] and [39]. Morespecifically, we use the MATLAB implementations of PESQand PEAQ provided in [40] and [41] for our verifications. Theexplanations of the output scores from these PESQ and PEAQimplementations are given in Table II. Both scores are relatedto the mean opinion scores [42].

For each noise induced test signal, PESQ or PEAQ valuesare computed. For comparison, we also evaluated test signalsinjected with white noise at different fullband signal-to-noiseratio (SNR) of 60 dB, 40 dB and 20 dB, respectively. The resultsare given in Table III.

From Table III, it is seen that the generated probe noise israted somewhere between imperceptible and perceptible but notannoying, which is very satisfactory. On the other hand, usingwhite noise as probe noise, the SNR must be somewhere be-tween 40 and 60 dB in order to obtain similar sound quality.However, the fullband SNRs between the test signals and theperceptually generated probe noise signals are generally foundto be 20–25 dB. Thus, shaping the probe noise in a perceptualrelevant manner, it is possible to inject an inaudible probe noisewith higher signal power compared to using white noise as probenoise.

4) Enhancement Filter Estimation: In our simulations, thetime-varying enhancement filter is estimated based on theerror signal , according to (12). The estimated filter coef-ficients are then copied to different blocks indicated by inFigs. 1–4. The length of is chosen to be , and

is used. Thereby, the requirement of in (11) is ful-filled.

For simplicity, we used the same SAF approach, as inSection IV-B-2, to estimate the nonzero part of the enhance-ment filter with a length-64 adaptive filter. The subbandNLMS step size is used for all subbands except forthe lowest one, where the step size is set to 0.

C. Simulation Results and Discussions

Five simulation experiments are carried out. In the first exper-iment, we set in Fig. 1, this gives an idealworking situation for the hearing aid without acoustic feedback.In the remaining four experiments, the loudspeaker signal is fedback to the microphones through the acoustic feedback paths

as shown in Fig. 6, and AFC is carried out using the dif-ferent approaches illustrated in Figs. 1–4. The duration of thesimulation is 150 s, and the transition of the feedback paths

from the normal to the telephone situation takes placeafter 50 s. As mentioned, the step sizes for estimation ofare adjusted so that the same steady-state error would be ob-tained in all approaches.

1) Howling Suppression: First, we evaluate the abilities tosuppress howling by examining the loudspeaker signals fromthe different AFC approaches. In Fig. 8, the spectrograms areshown for a selected time period and frequency region of theloudspeaker signals from all five simulations. The selected timeperiod includes the transition of the acoustic feedback paths

after 50 s, and the selected frequency region 0–6 kHz in-cludes the most significant differences among the approaches. Itis expected that the system would become unstable, and howlingoccurs, shortly after the transition, until the AFC system againstabilizes the system by adapting to the new acoustic feedbackpaths.

Comparing Fig. 8(b) to the reference loudspeaker signal inFig. 8(a), it is seen that using the T-AFC approach shown inFig. 1, severe sound distortions are introduced in the resultingloudspeaker signal. The distortion is present before the tele-phone-to-ear transition at 50 s, and it is caused by biased esti-mation of , because the incoming signals have very domi-nant spectral peaks, especially around 2.5 kHz, which leads to anonzero correlation between the loudspeaker signal and the in-coming signal (despite the hearing aid processing delay of 6 ms).Furthermore, howling occurs after the feedback path transition


Fig. 8. The spectrograms of the loudspeaker signal in a hearing aid system.The window size is 512 samples with 50% overlap, and a Hanning window isapplied. (a) The reference—without acoustic feedback and AFC. (b) The tradi-tional AFC approach (T-AFC). (c) The traditional probe noise approach (T-PN).(d) The proposed probe noise approach I (PN-I). (e) The proposed probe noiseapproach II (PN-II).

at 50 s, reflected by the additional tonal components in the loud-speaker signal after the transition.

Comparing the results from the T-PN approach shown inFig. 8(c) to the reference signal in Fig. 8(a), no severe sounddistortions are observed before the feedback path transitionat 50 s. This is a significant improvement compared to thetraditional AFC approach shown in Fig. 8(b) and is achievedbecause the T-PN approach guarantees unbiased estimation,and because the true feedback paths are stationary, such thatthe slow convergence rate of T-PN approach is not revealed.However, the system becomes unstable after the transition, asseen by the additional tonal component found at approximately2.5 kHz after 50 s in Fig. 8(c). The howling disappears overtime, although it can not be seen in Fig. 8(c). The long howlingtime is caused by the slow convergence rate of the T-PNapproach due to the low probe noise to disturbing signal ratio.

Fig. 9. Evaluation of different AFC approaches using � �� at 2.5 kHz.

This is an example where the T-PN approach faces significantdifficulties in practical applications.

Using the PN-I approach, the howling after the feedback pathtransition is not completely eliminated, as seen in Fig. 8(d).However, it is canceled within 1 s by the AFC system. This issignificantly shorter than the case for the T-PN approach. Oth-erwise, no noteworthy signal distortion is observed from thisimproved approach.

Finally, using the PN-II approach as shown in Fig. 8(e), thehowling is almost avoided after the feedback path transition;the howling is only barely observed after the feedback pathtransition due to the further increased convergence rate in thisapproach.

2) Convergence Over Frequencies: We evaluate further thedifferent AFC approaches objectively by using a performancemeasure, similar to the PTF expression in (17), defined as

(37)

The magnitude of the open-loop transfer function is given by. To ensure system stability, the

forward path gain for each frequency and time indexcan be limited to , so that

. This gain limit can be considered as an instantaneous gainmargin, which provides the maximum possible gain in the for-ward path before the system might become unstable; ob-viously, a relatively large gain margin is desired.

In Fig. 9, we show at 2.5 kHz, where the incomingsignals have the most spectral energy and the enhancementfilter has most of its effect around this specific frequency. Itis clear that has a high steady-state value when usingthe T-AFC approach due to the bias problem. Using the T-PNapproach, converges over time, but only at a very slowspeed. On the other hand, the convergence rate is significantlyincreased, by a factor of approximately 6 in this example usingthe PN-I approach; an additional improvement by a factor ofmore than 1.6 is obtained in the PN-II approach. The curves inFig. 9 are computed based on a single simulation run and aretherefore less smooth than the curves in Fig. 5, which are theaverage of 100 simulation runs.


V. CONCLUSION

In this work, we dealt with probe noise based acousticfeedback cancellation approaches in a multiple-microphoneand single-loudspeaker audio system. Traditional probe noiseapproaches can be used to prevent the major problem of biasedadaptive filter estimation in acoustic feedback cancellation bybasing the estimation of acoustic feedback paths on a probenoise signal. However, the convergence rate is generally de-creased since the added probe noise must have low powerin order to be inaudible. In this paper, we presented and an-alyzed two probe noise based approaches. We showed thatboth approaches are capable of increasing the convergence ratesignificantly without compromising the desired steady-stateerror, by using a combination of an inaudible probe noisesignal with limited correlation time and the so-called probenoise enhancement filters designed as long-term predictionerror filters. This is verified by simulation experiments, wherethe proposed probe noise approach I increases the convergencerate by a factor of 6 compared to the traditional probe noiseapproach, and the proposed probe noise approach II increasesthe convergence rate further by a factor of 1.6, whereas thetraditional acoustic feedback cancellation approach withoutprobe noise completely fails due to the bias problem. Further-more, we demonstrated through simulation experiments thatthese proposed approaches are applicable to acoustic feedbackcancellation in a realistic hearing aid system.

We believe that the proposed probe noise approaches, whichprovide unbiased estimation with much higher convergence ratethan the traditional probe noise approaches, bring us closer to acomplete solution of the biased estimation problem in closed-loop hearing aid systems. The idea behind these approachescould also be applicable in other closed-loop applications suchas public address systems and in open-loop acoustic echo can-cellation systems. These are considered as future work, whichalso include a comparison between the proposed approaches andexisting AFC systems in terms of cancellation performance andcomputational complexity.

APPENDIX ACONSTRAINT ON ENHANCEMENT FILTER TO ENSURE

UNBIASED ESTIMATION

In this appendix, we show that by using the constraint given in(11), an unbiased estimation of is guaranteed in the PN-Iapproach.

Recall that is uncorrelated with the incoming signalsand the original loudspeaker signal . Then, using (24)

and (19), the expected value of can be expressed by

(38)

It is seen that the expectation termin (38) follows a standard LMS algo-

rithm and therefore provides an unbiased estimation of .However, we need to consider the last term of

in (38), which occurs due to the intro-duction of the enhancement filter , where the desired filteredprobe noise signal can be modified by

and thereby may introduce a bias in . Introducingthe vector

, its element is given by

(39)

The last term in (38) can now be written as

(40)

The expected value is further expressedby (41), (See equation at bottom of page) where we use thenotation . It follows that

because is generated using an ordershaping filter . Thus, it can be seen from (41) that allentries in the columns through of the matrix

are equal to zero because these entriesonly involve the autocorrelation values . Itmeans that by imposing the constraint introduced in (11), thevector in (40) and (38)equals a null-vector. It is now seen that (38) follows a standard

......

. . ....

(41)


LMS algorithm and thereby provides an unbiased estimation of[3].

APPENDIX BINFLUENCE OF ENHANCEMENT FILTER ON PROBE NOISE

Under the constraint of in (11), we showthat .

Define . It follows that

......

...

(42)

where we defined and in Section III-B-1. Eq.(42) is valid because the first samples of

are zeros and .

ACKNOWLEDGMENT

The authors would like to thank the reviewers and the asso-ciate editor for their valuable suggestions and comments.

Furthermore, M. Guo would like to thank T. B. Elmedyb fordiscussing the initial idea of this work.

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Meng Guo (S’10) received the M.Sc. degree in ap-plied mathematics from the Technical University ofDenmark, Lyngby, Denmark, in 2006.

From 2007 to 2010, he was with Oticon A/S,Smørum, Denmark, as a research and developmentengineer in the area of acoustic signal processingfor hearing aid applications, especially in algorithmdesign of acoustic feedback cancellation. Currently,he is an industrial Ph.D. fellow with Aalborg Uni-versity, Aalborg, Denmark, and Oticon A/S. Hismain research interests are in the area of acoustic

signal processing, including acoustic feedback cancellation, acoustic echocancellation, adaptive filtering techniques and auditory signal processing.

Søren Holdt Jensen (S’87–M’88–SM’00) receivedthe M.Sc. degree in electrical engineering from Aal-borg University, Aalborg, Denmark, in 1988, and thePh.D. degree in signal processing from the TechnicalUniversity of Denmark, Lyngby, Denmark, in 1995.

Before joining the Department of ElectronicSystems of Aalborg University, he was with theTelecommunications Laboratory of Telecom Den-mark, Ltd, Copenhagen, Denmark; the ElectronicsInstitute of the Technical University of Denmark; theScientific Computing Group of Danish Computing

Center for Research and Education (UNI•C), Lyngby, Denmark; the ElectricalEngineering Department of Katholieke Universiteit Leuven, Leuven, Belgium;and the Center for PersonKommunikation (CPK) of Aalborg University. He isFull Professor and is currently heading a research team working in the area ofnumerical algorithms, optimization, and statistical signal processing for speech

and audio processing, image and video processing, multimedia technologies,and digital communications.

Prof. Jensen was an Associate Editor for the IEEE TRANSACTIONS ON SIGNAL

PROCESSING and Elsevier Signal Processing, and is currently Associate Editorfor the IEEE TRANSACTIONS ON AUDIO, SPEECH AND LANGUAGE PROCESSING

and EURASIP Journal on Advances in Signal Processing. He is a recipient of anEuropean Community Marie Curie Fellowship, former Chairman of the IEEEDenmark Section, and Founder and Chairman of the IEEE Denmark Section’sSignal Processing Chapter. He is member of the Danish Academy of TechnicalSciences and was in January 2011 appointed as member of the Danish Councilfor Independent Research—Technology and Production Sciences by the DanishMinister for Science, Technology and Innovation.

Jesper Jensen received the M.Sc. degree in electricalengineering and the Ph.D. degree in signal processingfrom Aalborg University, Aalborg, Denmark, in 1996and 2000, respectively.

From 1996 to 2000, he was with the Center forPersonKommunikation (CPK), Aalborg University,as a Ph.D. student and assistant research professor.From 2000 to 2007 he was a post-doctoral researcherand assistant professor with Delft University ofTechnology, Delft, The Netherlands, and an ex-ternal associate professor with Aalborg University.

Currently, he is with Oticon A/S, Smørum, Denmark. His main researchinterests are in the area of acoustic signal processing, including signal retrievalfrom noisy observations, coding, speech and audio synthesis, intelligibilityenhancement of speech signals and perceptual aspects of signal processing.

ieee transactions on audio, speech, and language...

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