# Noninvasive Model Independent Noise Control  with Adaptive Feedback Cancellation

Authors: Jing Yuan
Journal: Advances in Acoustics and Vibration
 (2008-02-24)

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## Abstract

An active noise control (ANC) system is model dependent/independent if its controller transfer function is dependent/independent on initial estimates of path models in a sound field. Since parameters of path models in a sound field will change when boundary conditions of the sound field change, model-independent ANC systems (MIANC) are able to tolerate variations of boundary conditions in sound fields and more reliable than model-dependent counterparts. A possible way to implement MIANC systems is online path modeling. Many such systems require invasive probing signals (persistent excitations) to obtain accurate estimates of path models. In this study, a noninvasive MIANC system is proposed. It uses online path estimates to cancel feedback, recover reference signal, and optimize a stable controller in the minimum
H2 norm sense, without any forms of persistent excitations. Theoretical analysis and experimental results are presented to demonstrate the stable control performance of the proposed system.


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## Body

## 1. Introduction

Most active noise control (ANC)
systems are model dependent. LetP^(z) and S^(z) denote estimates of primary and secondary path
transfer functions P(z) and S(z). Either S^(z) or both P^(z) and S^(z) must be obtained by initial system identification for model-dependent ANC systems. Controller
transfer function C(z) of a model-dependent ANC system is
either designed by minimizing ∥P^(z)+S^(z)C(z)∥, or adapted with the aid of S^(z) [1, 2].
If estimates P^(z) and S^(z) contain too much error, a model-dependent ANC system may generate constructive instead of
destructive interference. This is mathematically equivalent to ∥P(z)+S(z)C(z)∥>∥P(z)∥
even if ∥P^(z)+S^(z)C(z)∥ is minimized. If phase error in S^(z) exceeds 90∘ in some frequency, an ANC
system adapted by the filtered-X least mean square (FXLMS) algorithm may become
unstable [3–5].
An operator of a model-dependent ANC system must have the knowledge and skill
to obtain accurate estimates of path models by initial system
identification for each individual application.During the operation of an ANC
system, changes of environmental or boundary conditions may cause significant
changes to path transfer functionsP(z) and S(z). Since a model-dependent
ANC system only remembers initial path estimates P^(z) and S^(z),
variation of P(z) and S(z) may cause mismatch
with initial estimates P^(z) and S^(z) to degrade ANC performance. In cases of severe
mismatch between path transfer functions and their initial estimates, a model-dependent
ANC system may generate constructive instead of destructive interference, or
even become unstable.Model-independent ANC (MIANC) systems
depend on online path modeling or invariant properties of sound fields to update
or design controllers [6–8].
These systems avoid initial path modeling and are adaptive to variations of
environmental or boundary conditions of sound fields. Many adaptive MIANC systems require invasive persistent excitations to obtain accurate path estimates and ensure closed-loop stability
[6, 7, 9, 10].
Noninvasive MIANC systems are able to ensure closed-loop stability without persistent excitations,
which are
possible by a recently developed algorithm, known as orthogonal
adaptation [11, 12],
if the primary noise signal is directly available as the reference signal.In many real applications, the primary
noise signal is not necessarily available and the reference signal must be recovered
from the
sound field [1, 2]. When an ANC system is active, a
measured signal is a linear combination of primary and secondary signals. Feedback
of ANC
signal in the measurement is mathematically modeled by a feedback transfer
function F(z) from the controller to the reference sensor. Accurate estimation
of F(z) is as important as accurate estimation of P(z) or S(z)
[9, 13]. A complete noninvasive MIANC (CNMIANC) system must be able to
suppress the noise signal without injecting probing signals for online modeling
of P(z), S(z), and F(z). Most
available methods for adaptive feedback cancellation require persistent
excitations [9, 13]. In
this study, a new method is presented for adaptive feedback cancellation without
persistent excitations.It was proposed to use a pair of sensors
to measure pressure signals in ducts, from which traveling waves are resolved
[14, 15]. The
outbound wave could be used directly as the reference signal without cancelling
feedback signals if an infinite-impulse-response (IIR) controller could be
implemented accurately [14, 15]. In reality, it is very difficult to implement
a stable ideal IIR ANC controller [16]. Most practical ANC systems use
finite-impulse-response (FIR) controllers. The outbound wave in a duct is a
linear combination of primary noise and reflected version of feedback signal. Instead
of using the outbound wave directly as the reference, the least mean square
(LMS) algorithm is applied in this study to cancel feedback signals in the
outbound wave before using it as the reference. Orthogonal adaptation is combined
with the proposed ANC configuration to implement a CNMIANC system. Experimental
result is presented to demonstrate the performance of the CNMIANC system.


## 2. System Configuration and Model

Figure1 illustrates the configuration of the proposed ANC system.
The primary source is represented by the upstream speaker and the secondary
source is the midstream speaker. Cross-sectional area of the duct is small
enough such that sound field in the duct can be modeled by a 1D sound field in
the frequency range of interest. Three microphone sensors are installed in the
duct, measuring signals p1, p2,  and p3, respectively. Since the
primary noise signal is not available to the ANC system, the reference signal is recovered
from p1 and p2,  while p3 is the error signal to be
minimized by the ANC system.Figure 1
Configuration of the proposed MIANC system.Letd denote the axial distance between p1 and p2. The acoustical two-port theory [16, 17] has been applied by many
ANC researchers for the design and analysis of ANC systems. It is adopted here
as an analytical tool. An equivalent acoustical circuit is shown in
Figure 2 to
model the two-microphone system. The upstream part, from the primary source to
location of p1, is
equivalent to an acoustical source with strength up  and impedance Zp.
The downstream part, from location of p2  to the outlet, is represented by another acoustical source with strength us and impedance Zs. Characteristic
impedance of the duct is represented by Zo.(a) Acoustical two-port circuit in the duct
system, (b) contribution by controller, and (c) contribution by primary source.
(a)(b)(c)The linear system theory allows one to solvep1 and p2 in Figure 2(a) by focusing on acoustical circuits of
Figures 2(b) and 2(c) before adding two solutions together as the final solution
of Figure 2(a). For the case of up=0,
which is represented by Figure 2(b), one obtains (1)p2|up=0=[cos⁡(kd)+jZoZpsin⁡(kd)]p1|up=0,us−p2|up=0=[ZsZpcos⁡(kd)+jZsZosin⁡(kd)]p1|up=0, where k is the wave number. One can solve, from (1),(2)p2|up=0=Zo[Zpcos⁡(kd)+jZosin⁡(kd)](Zs+Zp)Zocos⁡(kd)+j(ZsZp+Zo2)sin⁡(kd)us,(3)p1|up=0=ZoZp(Zs+Zp)Zocos⁡(kd)+j(ZsZp+Zo2)sin⁡(kd)us.Similarly, for the case of us=0, which is represented by
Figure 2(c), one obtains (4)p1|us=0=[cos⁡(kd)+jZoZpsin⁡(kd)]p2|us=0,up−p1|us=0=[ZpZscos⁡(kd)+jZpZosin⁡(kd)]p2|us=0, from which one can solve(5)p1|us=0=Zo[Zscos⁡(kd)+jZosin⁡(kd)](Zs+Zp)Zocos⁡(kd)+j(ZsZp+Zo2)sin⁡(kd)up,(6)p2|us=0=ZoZs(Zs+Zp)Zocos⁡(kd)+j(ZsZp+Zo2)sin⁡(kd)up.Adding (2) and (6), one may write(7)p2⁢=p2|up=0+p2|us=0=Zo[Zpcos⁡(kd)+jZosin⁡(kd)]us+ZoZsup(Zs+Zp)Zocos⁡(kd)+j(ZsZp+Zo2)sin⁡(kd).The same method is applicable to
(3) and (5) for(8)p1⁢=p1|up=0+p1|us=0=Zo[Zscos⁡(kd)+jZosin⁡(kd)]up+ZoZpus(Zs+Zp)Zocos⁡(kd)+j(ZsZp+Zo2)sin⁡(kd).The next step
is to use complex factor α=Zo/((Zs+Zp)Zocos(kd)+j(ZsZp+Zo2)sin(kd)) to simplify (7) and (8). The results read(9)p2=α{[Zpcos⁡(kd)+jZosin⁡(kd)]us+Zsup},p1=α{[Zscos⁡(kd)+jZosin⁡(kd)]up+Zpus}. Since cos(kd)=0.5(ejkd+e−jkd)
and jsin(kd)=0.5(ejkd−e−jkd),
(9)  can be written as(10)p2=α{[Zp+Zo2ejkd+Zp−Zo2e−jkd]us+[Zs+Zo2+Zs−Zo2]up},p1=α{[Zs+Zo2ejkd+Zs−Zo2e−jkd]up+[Zp+Zo2+Zp−Zo2]us}.Let(11)wi=α{Zs−Zo2up+Zp+Zo2ejkdus}(12)wo=α{Zp−Zo2us+Zs+Zo2ejkdup} represent the in- and outbound
waves in the duct. By comparing (10)
with (11) and (12), one can see
that (10)  are equivalent to(13)p2=wi+woe−jkd,p1=wie−jkd+wo. The in- and outbound waves can be
resolved from p1 and p2 via(14)[wiwo]=[e−jkd11e−jkd]−1[p1p2]=11−e−2jkd[−e−jkd11−e−jkd][p1p2].In a digital
implementation of ANC system, it is recommended to select sampling intervalδt such that
its product with sound speed c satisfies cδt=d. As a result, the delay operator exp(−jkd)=z−1 becomes an exact one-sample delay for discrete-time
ANC systems.


## 3. Feedback Cancellation

It is indicated
by (12) that the outbound wave contains feedback from us that must be cancelled to recover the reference signal. Let R1=(Zp−Zo)/(Zp+Zo) denote the upstream reflection coefficient. By
multiplying e−jkdR1 to (11), one obtains(15)e−jkdR1wi=α{(Zs−Zo)(Zp−Zo)2(Zp+Zo)e−jkdup+Zp−Zo2us}.A subtraction of (15) from (12) enables
one to
write(16)wo−e−jkdR1wi=n,where(17)n=α[(Zs+Zo)(Zp+Zo)ejkd−(Zs−Zo)(Zp−Zo)e−jkd]2(Zp+Zo)up is only contributed by the
primary source up.Usingcos(kd)=0.5(ejkd+e−jkd)
and jsin(kd)=0.5(ejkd−e−jkd),
one can see that the common denominator of p1, p2, and all transfer
functions in the duct is(18)(Zs+Zp)Zocos⁡(kd)+j(ZsZp+Zo2)sin⁡(kd)=0.5(Zs+Zo)(Zp+Zo)ejkd−0.5(Zs−Zo)(Zp−Zo)e−jkd.Substituting (18) into the
definition of α (immediately after (8)), one obtains(19)2Zo=α[(Zs+Zo)(Zp+Zo)ejkd−(Zs−Zo)(Zp−Zo)e−jkd].A further substitution of (19)
into (17) leads to(20)n=ZoupZp+Zo.This is the reference signal to
be recovered by the proposed ANC system.A question to
be answered here is why not recovering the reference signal from a pressure
signal such asp1. The hint is
(8) that may be expressed as p1=F(jω)us+B(jω)up.
In view of (8), the acoustical feedback transfer function is(21)F(jω)=ZoZp(Zs+Zp)Zocos⁡(kd)+j(ZsZp+Zo2)sin⁡(kd).Since F(jω) is a transfer function with resonant
poles, it has an infinite impulse response (IIR). In many ANC systems, a finite-impulse-response
(FIR) filter F^(jω) is used to approximate F(jω). This means inevitable approximation
errors in the first place.Besides, all
transfer functions in a duct are sensitive to values ofZo, Zs, and Zp. In particular, Zs is the impedance of the
entire downstream segment from the location of p2 to the duct outlet. Objects moving near the duct
outlet could cause changes of Zs.
A fracture in any downstream part may also cause a significant change to Zs as well. If initial
estimate F^(jω) is remembered by an ANC system, it is a
stability issue how significant will F(jω)−F^(jω) turn
out as a result of a small variation of Zs. An indicative answer might be(22)∂∂ZsF(jω)=−ZoZp[Zocos⁡(kd)+jZpsin⁡(kd)][(Zs+Zp)Zocos⁡(kd)+j(ZsZp+Zo2)sin⁡(kd)]2.The common denominator of p1, p2, and all transfer functions in the duct has an
alternative form in (18), which is equivalent to(23)⤢0.5(Zs+Zo)(Zp+Zo)ejkd−0.5(Zs−Zo)(Zp−Zo)e−jkd=0.5(Zs+Zo)(Zp+Zo)ejkd[1−(Zs−Zo)(Zp−Zo)(Zs+Zo)(Zp+Zo)e−2jkd]=0.5(Zs+Zo)(Zp+Zo)ejkd[1−R1R2e−2jkd], where R2=(Zs−Zo)/(Zs+Zo) represents the downstream reflection coefficient.Since resonant
frequencies of the duct are roots of the common denominator, it is suggested by
(22) and (23) that all transfer functions in the duct, including the feedback
transfer function F(jω), are
sensitive to variance of Zs at the resonant peaks. The stronger the resonance, the more sensitive of
transfer functions with respect to Zs.
If an ANC system recovers the reference signal from a pressure signal like p1, a small online variation
of Zs may cause a
significant mismatch between F(jω) and
initial estimate F^(z).
As a result, closed-loop stability is sensitive to possible variation of Zs.If the
reference signal is recovered from traveling waves with (16), the situation
will be different. In a discrete-time implementation, one may rewrite (16) to n(z)=wo−Fw(z)wi,  where the acoustical feedback transfer function is a delayed version of
upstream reflection coefficient Fw(z)=z−1R1(z). Here, R1=(Zp−Zo)/(Zp+Zo) is only sensitive to Zp and Zo.
Characteristic impedance Zo is a real constant depending on sound speed and cross-sectional area between p1 and p2. It seldom changes significantly in online ANC
operations. As for Zp, it is
the impedance of the upstream portion from the primary source to the location
of p1. In most
applications, p1 and  p2  are measured as close as
possible to the primary source. Impedance Zp is deeply hidden in a very short segment of the duct. Its variation, if any,
would be certainly not as significant as that of Zs.No matter how
significant are the possible variations ofZp or Zo,
the passive upstream reflection always has a limited magnitude |R1|<1. For each pair of fixed Zp and Zo, |R1(jω)| does not have sharp peaks or dips as a
function of ω. In many cases, |R1|             is constant for a pair of fixed  Zp and Zo. Let X(jω) denote
the Fourier transform of x(t), then X(jω)=L{x(t)}
and x(t)=L−1{X(jω)}  share
many similar properties. For example, if x(t) is a low-frequency function of t, then the bandwidth of X(jω) is narrow in terms of ω. Similarly,
if X(jω) is a
“low-frequency”  function of ω, then the time duration of x(t)
is short (a narrow bandwidth in terms of t).
The fact that |R1|  is a
“low-frequency" function of ω for
each pair of fixed Zp and Zo   implies short impulse
responses of R1(z). It is, therefore, reasonable to
assume that R1(z)=∑k=0mrkz−k can be approximated by a FIR transfer function
with negligible errors (Assumption A1). If both Zp and Zo are constant, R1  is a
single constant. Resonant effects in the duct are hidden in wave signals wi and wo without affecting R1.
This is a major difference between recovering the reference signal from
traveling waves and recovering the reference signal from a pressure signal.Even if an estimate ofFw(z) is obtained by initial
identification, it is less likely that online variations of environmental or
boundary conditions could cause significant mismatch between Fw(z) and its initial estimate. The resultant ANC system is semimodel
independent if its reference signal is recovered with (16) in combination with
a MIANC adaptation algorithm such as orthogonal adaptation.


## 4. Complete Noninvasive MIANC

Noninvasive model-independent feedback cancellation is possible by applying
LMS to (16). With assumption A1, online estimate of the feedback transfer
function is represented by polynomial(24)R^(z)=∑k=0mr^k(t)z−k,where rk(t) is the kth coefficient for the tth sample. An estimated version of (16)
would be (25)n^=wo−z−1R^(z)wi,which has a discrete-time domain
expression,(26)n^(t)=wo(t)−∑k=0mr^k(t)wi(t−k−1).Coefficients of R^(z)=∑k=0mr^k(t)z−k are updated with the LMS algorithm as follows:(27)r^k(t+1)=r^k(t)+μn^(t)wi(t−k−1),where μ>0 is a
small constant representing the LMS step size. Since R1(z)=∑k=0mrkz−k by assumption A1, the discrete-time domain
version of (16) is(28)n(t)=wo(t)−∑k=0mrkwi(t−k−1).Subtracting (28) from (27), one
obtains(29)n^(t)−n(t)=∑k=0m[rk−r^k(t)]wi(t−k−1)=∑k=0mΔrk(t)wi(t−k−1),where Δrk(t)=rk−r^k(t) is the estimation error of rk. Let Δr=[Δr0,Δr1,…,Δrm]T  and let ϖi(t)=[wi(t−1),wi(t−2),wi(t−m−1)]T. It is possible to express
(29) in an inner product(30)n^(t)−n(t)=ΔrTϖi(t).Estimation residues of LMS
algorithms are usually expressed as inner products like (30). It has been
proven that the LMS algorithm is able to drive the convergence of these inner
products towards zero.If the primary noise signalup was available, mathematical model of the error signal
may be expressed in the discrete-time z-transform domain as e(z)=P(z)up(z)+S(z)us(z), where the actuation signal would be synthesized as us(z)=C(z)up(z). Since up is actually not available, the ANC system has to
recover n^(z) from the outbound wave and then synthesize us(z)=C(z)n^(z) instead. After the convergence of n^(z)→n (z), one may express the mathematical
model of the error signal to(31)e(z)={P(z)[1+ZpZo]+S(z)C(z)}n(z),where (20)
has been substituted. Let H(z)=P(z)[1+Zp/Zo],
then (31) becomes(32)e(z)=[H(z)+S(z)C(z)]n(z). It is mathematically
equivalent to another ANC system whose primary source is available to the
controller as n(z), with primary path transfer function H(z) and secondary path
transfer function S(z). Orthogonal adaptation is readily
applicable to (32) to implement a noninvasive MIANC system.It is assumed thatH(z) and S(z) can be approximated
by FIR filters with negligible errors (Assumption A2). Let hT=[h0h1⋯hm]  and sT=[s0s1⋯sm] denote coefficients of H(z)
and S(z), respectively, the discrete-time domain version of e(z)=H(z)n(z)+S(z)us(z)  is a discrete-time convolution:(33)e(t)=∑k=0mhkn(t−k)−∑k=0mskus(t−k),where e(t),  n(t), and  us(t) denote
samples of e(z), n(z), and us(z),
respectively. Introducing coefficient vector θT=[hTsT] and regression vector ϕt=[n(t)n(t−1)⋯n(t−m),us(t)us(t−1)⋯us(t−m)]T, one may rewrite (33) to (34)e(t)=θTϕt. Let H^(z) and S^(z) denote online estimates of H(z)
and S(z). Path estimates H^(z) and S^(z) are obtained by minimizing estimation error as
follows:(35)ε(z)=e(z)−H^(z)n(z)−S^(z)us(z)=ΔH(z)n(z)+ΔS(z)us(z),where ΔH(z)=H(z)−H^(z) and ΔS(z)=S(z)−S^(z) are online modeling errors. Let θ^T=[h^Ts^T] denote online estimate of θT=[hTsT], then h^T=[h^0h^1⋯h^m]h^0h^1⋯h^m  and s^T=[s^0s^1⋯s^m]s^0s^1⋯s^m represent the coefficients of H^(z) and S^(z),
respectively. Similar to the equivalence between (34) and e(z)=H(z)n(z)+S(z)us(z),  (35) has
a discrete-time domain equivalence(36)εt=e(t)−θ^Tϕt=Δθ^Tϕt,where Δθ=θ−θ^ is the online coefficient error vector. The entire
CNMIANC system performs three online tasks that are mathematically represented
by the minimization of three inner products. The first is inner product given
in (30); the second one is given in (36); and the third one is θ^Tϕt.Equations (30)
and (36) contain estimation errors Δr and Δθ. Most
available estimation algorithms, such as LMS and the recursive least squares
(RLS), are very capable of driving inner products like (30) and (36) towards
zero, or at least minimizing their magnitudes [18].
A difficult problem is how to force Δr→ 0 and Δθ→ 0. Available
solutions inject significant levels of   “persistent excitations”  (invasive probing
signals) to the estimation system [6, 7, 9, 10, 13]. A unique feature of the
proposed CNMIANC is no persistent excitations. The system works well without
requiring Δr→  0 and Δθ→  0.For (30),
minimizing the inner product in the right-hand side implies convergence of n^→n in the left-hand side. It would be great if Δr→  0 as well. Otherwise, Δr may just converge
to a FIR filter that filters out wi from wo. On the other
hand, minimizing the inner product in (36) only implies εt→  0. The question is what does it further
implies? One may consider the equivalence between (34) and e(z)=H(z)n(z)+S(z)us(z), which holds
if one replaces θT=[hTsT], H(z),
and S(z) with respective estimates θ^T=[h^Ts^T], H^(z),
and S^(z).
The equivalence is now between forcing θ^Tϕt≈0 and forcing(37)H^(z)n(z)+S^(z)us(z)=[H^(z)+S^(z)C(z)]n(z)≈0.The CNMIANC system uses online
estimates of H^(z) and S^(z) to solve C(z) that minimizes ∥H^(z)+S^(z)C(z)∥2.
This is equivalent to forcing θ^Tϕt≈0.
One can obtain(38)‖e‖=‖εt+θ^Tϕt‖≤‖εt‖+‖θ^Tϕt‖ by adding θ^Tϕt to both sides of (36). As the CNMIANC system
drives εt=Δθ^Tϕt→ 0 and forces |θ^Tϕt|≈0 ultimately, it implies ultimate convergence of ∥e∥→ 0 even though Δθ does
not necessarily converge to zero [11, 12].


## 5. Experimental Verification

A CNMIANC system was implemented and
tested in an experiment, with a configuration shown in
Figure1. Cross-sectional
area of the duct was 12×15 cm2. Two microphones were placed
30 cm downstream
from the primary speaker with a space of d  = 10 cm
between p1 and p2.
The distance between p2 and the secondary speaker is represented by L in
Figure 1. To guarantee a causal ANC system, the value of L must satisfy L>2d such that the
outbound wave is at least two samples ahead of sound propagation in duct. The
sampling interval of the controller was 0.29 millisecond with a sampling frequency
of 3.448 Hz, which satisfies d = cδt with
c=344 m/s and exp(jkd) =  z. The cutoff
frequency of antialias filters was chosen to be 1200 Hz. The in- and
outbound waves were recovered from pressure signals with (14). The reference
signal was recovered with (25). Coefficients of R^(z) were adapted with (27). Another online
modeling process used (34) to obtain coefficients of H^(z) and S^(z). The ANC
transfer function was solved by online minimization of ∥H^(z)+S^(z)C(z)∥2. The CNMIANC
system was implemented in a dSPACE 1103 board.Error signale(t) and primary noise up(t)
were collected
as vectors e and up for three cases. In case 1, there was no control
action. In case 2, up(t) was available as the reference signal
for an ANC system to suppress noise in the duct. In case 3, up(t) was not available and the CNMIANC system had to recover n^(t) from p1 and p2 for controller
synthesis. For each respective case, power spectral densities (PSD’s) of e(t)
and up(t) were computed with a MATLAB command called
“pmtm()”. Computational results are denoted as vectors  Pe=pmtm(e)   and
Pp=pmtm(up), where argument vectors e and up represent measurement samples of e(t) and up(t). The normalized PSD of e(t) was calculated as
Pne=10log(Pe/Pp)
for all
three cases.Shown in Figure3 are normalized PSD of e(t) for the three cases. For case 1, normalized
PSD of e(t) is
represented by the dashed-black curve. For case 2, normalized PSD of e(t) is plotted with
the solid-gray curve. For case 3, normalized PSD of e(t) is
represented by the solid-black curve. Both ANC systems were able to suppress
noise with good control performance as seen in Figure 3. The proposed CNMIANC
has slightly worse performance since its reference was the recovered signal n^(t) instead of the true primary source up(t). This is a small price to pay in case up(t) is not
available to the ANC system. The proposed CNMIANC system was stable and able to
recover the reference and suppress noise without any persistent excitations.Figure 3
Normalized PSDs ofe(t) for (a) uncontrolled
case (dashed-black), (b) controlled case with up(t) available
(solid-gray), and (c) controlled case with recovered n^(t) (solid-black).The CNMIANC system was robust with respect to sudden parameter change in
the duct. In the experiment, the duct outlet was changed from completely open
to completely closed. Such a sudden change shifted all resonant frequencies in
the duct. Path transfer functions also changed suddenly. The CNMIANC system
remained stable and converged very quickly.


## 6. Conclusions

The primary source is not necessarily available as the reference signal
for ANC systems in all practical applications. When the primary source is not
available, the ANC system must recover the reference signal from a sound field to
which ANC is applied. Feedback cancellation is an important issue in ANC
systems that recover reference signals from sound fields. In most
MIANC systems, persistent excitations are required for online modeling of
feedback path model and adaptive feedback cancellation [9, 13]. In this study,
a CNMIANC system is proposed that recovers reference signal from traveling
waves without persistent excitations. The corresponding feedback path model is
the upstream reflection coefficient and hence closer to an FIR filter than
pressure feedback transfer functions (IIR path models in resonant ducts).
Theoretical analysis and experimental results are presented to demonstrate the
stable operation of the proposed CNMIANC system.



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*Source: 863603-2008-03-17.xml*