IMPROVED STABLE FEEDBACK ANC SYSTEM WITH

DYNAMIC SECONDARY PATH MODELING

Rogelio Bustamante-Bello

1,2

, Héctor M. Pérez-Meana

1

(1) Graduate Studies Section. ESIME Culhuacán, Instituto Politécnico Nacional. 1000 Santa Ana Ave. San Francisco

Culhuacán, C.P. 04430, Ciudad de México, México.

(2) Instituto Tecnológico y de Estudios Superiores de Monterrey Campus Ciudad de México. 222

Del Puente St., Ejidos de Huipulco, C.P. 14380, Ciudad de México, México.

Bohumil Psenicka

Universidad Nacional Autónoma de México, Facultad de Ingeniería, P. O. Box 70-389, Delegación Coyoacán, C.P.

04510 Ciudad de México, México.

Keywords: Active Noise Control (ANC), stable feedback ANC systems, Normalized Filtered X LMS algorithm

(NFXLMS), feedforward ANC systems, Normalized Filtered X LMS algorithm with Noise Addition

(NFXLMS-NA).

Abstract: This paper presents the development and DSP implementation of a stable ANC feedback system with on-

line secondary path modelling, using the Normalized Filtered-X Least Mean Square with Noise Addition

algorithm (NFXLMS-NA), for acoustic noise cancellation. In this paper, the feedforward and the feedback

ANC systems are described briefly; the basic of the FXLMS algorithm and its structure is discussed and the

new NFXLMS-NA algorithm is presented. The ANC system developed includes a conventional noise

predictor, a primary adaptive filter, a subsystem for dynamic secondary path modelling and the addition of

white noise signal in the FXLMS algorithm in a novel structure looking for stability into the system. The

system was developed for cancelling quasi-periodic acoustic noise; some experimental results for narrow-

band signal are included in order to show the desirable feature (stability) of the system. Proposed system

was implemented using a TMS320C30 evaluation module from TI. Finally, the paper includes the block

diagram of the ANC system, the structure of the program used in the implementation and some photographs

of the practical scheme and the equipment used in the tests.

1 INTRODUCTION

The active noise cancellation (ANC) involves

electro acoustic or electro mechanic systems that

cancel the primary noise based on the superposition

principle. In fact, a “pseudo-noise” is generated with

same amplitude but with contrary phase of the

original noise to be cancelled in a specific area

(quiet zone); the ANC attenuates low frequency

noise where passive systems result to be no efficient

at all. The amount of cancelled noise depends on the

amplitude and phase of the control signal generated;

a more complete discussion of the principles of

ANC can be found in (Widrow et al., 1975) (Kuo

and Morgan, 1996) (Elliot, 2001) (Farhang-

Boroujeny, 1998) (Haykin, 1996) (Solo and Kong,

1995).

In the digital signal processing field, there are

two basic types which allow to implement ANC

systems, feedforward and feedback ANC systems,

which are show in the blocks diagrams of Figs 1 and

2; in both systems, a digital filter coefficients vector

is adjusted to minimize an error signal, which is

stated as the noise signal minus the control signal.

A basic feedforward ANC system has two

sensors: one of these sensors picks up the primary

noise (also called the reference signal) on the

upstream of sound propagation and feed this signal

on to the system’s filter –the secondary source- in

order to generate a control signal. The system tries

to estimate the propagation paths –the primary path-

from the first sensor to second and, using the

reference signal, generate a signal to cancel out the

primary noise at the place of the second sensor –the

error sensor-.

191

Bustamante-Bello R., M. Pérez-Meana H. and Psenicka B. (2005).

IMPROVED STABLE FEEDBACK ANC SYSTEM WITH DYNAMIC SECONDARY PATH MODELING.

In Proceedings of the Second International Conference on Informatics in Control, Automation and Robotics - Signal Processing, Systems Modeling and

Control, pages 191-199

DOI: 10.5220/0001162901910199

Copyright

c

SciTePress

A feedback ANC system has only the error

sensor and its signal is used to reconstruct the

reference signal. This system uses an adaptive linear

predictor in order to generate its internal reference

signal; then, this signal is used by the filter to

generate a control signal. The proposed ANC system

only can estimate the signal present at the error

sensor and, since only narrow-band signals can be

predicted, this system is most effective to cancel out

narrow-band low-frequency noises (Kuo and

Morgan, 1996), (Elliot, 2001), (Haykin, 1996),

(Bustamante and Perez, 2002).

In both cases, adaptive algorithms are generally

used to estimate the filter coefficients that are

modelling the signals. In the digital signal

processing field, there are several adaptive

algorithms that allow to implement ANC systems;

however, the least mean square (LMS) type

algorithm originally proposed by Widrow (Widrow

et al., 1975) is the most popular in ANC systems for

its simplicity. This algorithm adjusts the coefficients

of a digital filter in order to minimize the signal

present at the error sensor.

However, in a real application, it is necessary to

know the path from the digital filter to the error

sensor because this path could change the control

signal. The basic ANC algorithm which considers

the effects of this path (usually called the secondary-

path),

)(zS is the Filtered-X LMS (FXLMS)

algorithm, in which the reference signal is changed

by a filter modelling the secondary-path and then it

is used by the LMS algorithm to estimate the

primary path model (Kuo and Morgan, 1996),

(Elliot, 2001), (Haykin, 1996).

Typically, the secondary path is estimated using off-

line modelling and then used in the ANC system.

Figure 1: Basic feedforward ANC system

Figure 2: Basic feedback ANC system

However, if the secondary-path is time-varying,

it is desirable to estimate this path on-line in order to

assure the stability and convergence of the adaptive

filter.

In this paper, we present the implementation of a

feedback system in a TMS320C30 DSP system

using a modified FXLMS algorithm. The secondary

path is estimated using on-line modelling and, in

order to enhance the stability of the system, white

noise is added to the FXLMS algorithm. Also, we

provide some experimental results of this ANC

system in a real environment. As an advantage, this

system use only one input and one output in order to

avoid the interference among the control signal and

the external reference signal presents in the

feedforward systems (Kuo and Morgan, 1996),

(Elliot, 2001), (Haykin, 1996), (Bustamante and

Perez, 2002), (Bustamante et al., 2003), (Rafaely

and Elliot, 1996).

2 THEORY

There are many algorithms that govern adaptive

filters in ANC systems. In the following proposal we

revise the basic theory of the Least Mean Square

(LMS) algorithm (Widrow et al., 1975) -

(Bustamante et al., 2003), the Normalized LMS

(NLMS) algorithm (Kuo and Morgan, 1996) -

(Haykin, 1996), the Filtered X LMS (FXLMS)

algorithm (Kuo and Morgan, 1996), (Elliot, 2001),

(Haykin, 1996), (Bustamante and Perez, 2002),

(Bustamante et al., 2003), the Normalized FXLMS

(NFXLMS) algorithm and the new NFXLMS with

Noise Addition (NFXLMS-NA); this last one

algorithm was used in our system in order to work

with the on-line identification process to modelling

the secondary path and, at the same time, get

stability into the system.

2.1 The LMS algorithm

This algorithm is one of the simplest regarding its

implementation, and in its simpler version, we have

the stochastic gradient LMS algorithm. Equations

(1)-(4) show the basic equations of the LMS

algorithm; its function is to search the optimum

adaptive filter coefficients

)(n

opt

ω

G

that minimize

the error signal )(ne . These equations show that it is

a recursive algorithm, which means that the present

value of the coefficients )1(

+nω

G

depends on the

previous one )(n

ω

G

; essentially, the LMS is a

gradient search based method (Widrow et al., 1975)

(Kuo and Morgan, 1996) (Elliot, 2001) (Farhang-

ICINCO 2005 - SIGNAL PROCESSING, SYSTEMS MODELING AND CONTROL

192

Boroujeny, 1998) (Haykin, 1996) (Solo and Kong,

1995).

[]

)(

ˆ

)()1( nnn ξµωω ∇−=+

G

G

(1)

Where:

)()(2)()(

ˆ

2

nenxnen

G

−=∇=∇ξ

(2)

And

)()(2)()1( nenxnn

G

G

G

µωω +=+

(3)

It is important to notice that

µ

should not be

very large in order to avoid the method’s divergence,

but it also should not be very small so that the

convergence time results too long; a good choice for

µ

is:

max

1

0

λ

µ <<

(4)

Where

max

λ

is the maximum eigenvalue of the

input signal autocorrelation matrix.

The convergence speed depends on the

eigenvalues

i

λ

of the input signal autocorrelation

matrix. It is important to mention that the

eigenvalues of the input signal are related directly

with the power of the signal and every

i

λ

gives a

different convergence mode; from literature related

with this topic can be observed that the slower time

constant is given by eq. (5) (Widrow et al., 1975)

(Kuo and Morgan, 1996) (Elliot, 2001) (Farhang-

Boroujeny, 1998) (Haykin, 1996) (Solo and Kong,

1995). If there are large eigenvalues spread in the

input signal autocorrelation matrix, the algorithm

will have larger convergence times and, as a result, it

will not be useful for practical implementation.

min

4

1

max

µλ

τ =

(5)

s

s

Reference Signal’s Eigenvalues Dispersion. For

an ANC system with fast convergence, the input

signal autocorrelation matrix )]()([ nxnx

⊗ should

have the distribution shown in (6).

⎟

⎟

⎟

⎟

⎟

⎠

⎞

⎜

⎜

⎜

⎜

⎜

⎝

⎛

=

n

R

λ

λ

λ

"

#%##

"

"

00

0

2

0

00

1

(6)

The samples will be uncorrelated by obtaining a

diagonal matrix, making the LMS’s processing

easier. It is also required that the difference between

the eigenvalues

),...,,(

21 n

λλλ

is minimum in

order to achieve a very low dispersion coefficient. If

the autocorrelation matrix of input signal )(nx has a

large eigenvalue spread, elliptical level curves result

within a two coefficients error surface. These curves

provide a larger trajectory to get to the center

(optimum solution), due to the fact that the

convergence direction found by the LMS is

perpendicular to the level curves (Fig 3). For a lower

eigenvalue spread the level curves acquire a near

circular form providing a shorter and more direct

trajectory to arrive to an optimum solution as it can

be seen in Fig 4. To achieve similar maximum and

minimum input signal’s eigenvalues

(

max

min

λλ ≈

) it is necessary to pre-process this

signal before introducing it to the algorithm.

Figure 3: Disperse eigenvalues’ level curves

Figure 4: Similar eigenvalues’ level curves

In our case, we added white noise to the

reference signal in order to change its characteristics

(Kuo and Morgan, 1996), (Elliot, 2001),

(Bustamante and Perez, 2002), (Bustamante et al.,

2003); it process will be explained ahead.

2.2 The Normalized LMS (NLMS)

Algorithm

The convergence time and stability of the adaptation

process of the LMS algorithm is governed by the

step size

µ

and the reference signal power (Kuo and

Morgan, 1996) (Elliot, 2001) (Farhang-Boroujeny,

1998) (Haykin, 1996). The maximum stable step

size

µ

is inversely proportional to the filter order

and the power of reference signal

)(nx

. One

important technique to do the stepsize independent

IMPROVED STABLE FEEDBACK ANC SYSTEM WITH DYNAMIC SECONDARY PATH MODELING

193

of the input signal while maintaining the desired

steady-state performance, independent of the

reference signal power, is know as the

normalized

LMS algorithm

(NLMS).

The algorithm NLMS consists on adjusting the

coefficients

)(n

ω

G

in the iteration (n + 1) using a

correction factor

()

1+∆ n

ω

G

that is “normalized” in

accordance with the square norm of the values of the

reference signal

)(nx

in the iteration n (eq. 7).

)()1()1( nnn

ω

ω

ω

GGG

−+=+∆

)()(

2

)(

1

nenx

nx

G

G

=

(7)

To control the change in the coefficients

)(n

ω

G

from an iteration to another without changing their

direction, it is introduced a real positive factor of

scaling denoted by

ψ

. This is, the change

()

1+∆ n

ω

G

is redefined as:

()

)()(

2

)(

1 nenx

nx

n

G

G

G

ψ

ω =+∆

(8)

Then, the NLMS algorithm is expressed as:

)()(

2

)(

)()1( nenx

nx

nn

G

G

G

G

ψ

ωω +=+

(9)

where 0 <

ψ

< 2.

It is important to emphasize that the NLMS

algorithm presents a convergence rate potentially

faster than the LMS algorithm with correlated or

decorrelated input samples. On the other hand, when

the values of the reference signal

)(nx

are small,

numeric problems are presented when

ψ

is dividing

for a small value of

2

)(nx

.

To solve this problem, the form of the NLMS

algorithm is modified adding a constant value to the

norm

2

)(nx

, according to the eq. (10).

)()(

2

)(

)()1( nenx

nxa

nn

G

G

G

G

+

+=+

ψ

ωω

(10)

Where a > 0.

2.3 The Filtered-X LMS (FXLMS)

Algorithm

As it was mentioned in section 1, since the

secondary path transfer function

)(zS

follows the

adaptive filter

)(zW

, the LMS algorithm must be

modified to ensure convergence (Kuo and Morgan,

1996), (Elliot, 2001), (Haykin, 1996), (Rafaely and

Elliot, 1996), (Zhang et al., 2001). Figures 5 and 6

show the feedforward and the feedback ANC system

with the secondary path

)(ns

.

Figure 5: Basic feedforward ANC system with secondary

path

There are different possible schemes that can be

used to compensate the effect of

)(ns

. The most

common scheme is to place an estimated filter

)(

ˆ

ns

in the reference signal path to the weight update of

the LMS algorithm, which realizes the usually called

Filtered-X LMS (FXLMS) algorithm.

Figure 6: Basic feedback ANC system with secondary

path

In order to obtain the equations that control the

FXLMS algorithm, we begin with the equation of

the error signal

)(ne

; according to the Fig. 5:

)()()()()()( nynsndnyndne ∗−=

′

−=

)]()([)()( nxnnsnd ∗∗−= ω

(11)

According to eq. (2) and using the eq. (11) for the

error signal, we get the gradient estimated for the

FXLMS algorithm:

)()(2)(

ˆ

nenxn

′

−=∇

G

ξ

(12)

Where

)(nx

′

is the filtered reference signal and

is given by:

)()()( nxnsnx ∗=

′

(13)

Substituting Eq. (12) into Eq. (1), we get the

equation of the FXLMS algorithms for the

feedforward ANC system:

)()(2)()1( nenxnn

′

+=+

G

G

G

µωω

(14)

For the feedback ANC system, we can write the

equation for the FXLMS algorithm, as follows:

)()(

ˆ

2)()1( nenxnn

′

+=+

G

G

G

µωω

(15)

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194

Where

)(

ˆ

nx

′

, the estimated filtered reference

signal, is given by:

)(

ˆ

)()(

ˆ

nxnsnx

∗=

′

(16)

The estimated reference signal

)(

ˆ

nx

is showed

in the block diagram of the Fig 8 and it will be

compute later.

Figure 7: Feedforward ANC system with real secondary

path and estimated secondary path

Figure 8: Feedback ANC system with real secondary path

and estimated secondary path

Feedforward and feedback systems with off-line

estimated secondary path are showed in blocks

diagrams of Figs 7 and 8.

2.4 The Normalized FXLMS

(NFXLMS) Algorithm

Because the normalization technique optimizes the

convergence speed of the LMS algorithm, this

technique is used with the FXLMS algorithm in

order to improve the adaptation process. Equation

(17) shows the NFXLMS algorithm used in our

feedback ANC system.

)()(

ˆ

2

)(

ˆ

)()1( nenx

nxa

nn

′

′

+

+=+

G

G

G

G

ψ

ωω

(17)

2.5 The FXLMS Algorithm and the

Secondary Path ModelLing

The FXLMS algorithm requires knowledge of the

transfer function

)(zS

. There are two main

techniques to estimate that transfer function, the off-

line modelling and the on-line modelling; both

schemes are discussed briefly ahead (Kuo and

Morgan, 1996), (Elliot, 2001), (Haykin, 1996),

(Rafaely and Elliot, 1996), (Zhang et al., 2001).

2.5.1 Off-line modelling

Assuming that the characteristics of

)(zS

are time-

invariant but unknown, off-line modelling can be

used to estimated the secondary path during an

initial training stage. White noise is an ideal

broadband training signal in system identification

because it has a constant spectral density at all

frequencies; at the end of the training interval, the

estimated model

)(

ˆ

zS

is fixed and used for ANC

operation. Because this technique was not used in

our system, it will not be described anymore, but in

references (Kuo and Morgan, 1996), (Elliot, 2001)

there are some examples about the characteristics of

this technique.

2.5.2 On-line modelling

In some applications, the secondary path

)(zS

may

be time-varying. For this reason, it is desirable to

estimate the secondary path when the ANC system

is in operation, in order to assure the stability and

convergence of the adaptive filter. There are

different techniques to do that, but the more useful

technique is when the system use additive white

noise as an excitation signal for on-line modelling,

because those signal has a constant spectral density

at all frequencies.

A feedback ANC system using the FXLMS

algorithm with adaptive on-line secondary-path

modelling is showed in Fig. 9. A random noise

generator is used to generated a zero-mean white

noise )(nr that is uncorrelated with the estimated

primary noise )(

ˆ

nx . The white noise signal is added

to the control signal )(ny produced by the adaptive

filter )(nw to drive the secondary source. The

adaptive filter )(

ˆ

ns is connected in parallel with the

secondary path in order to be able to model

)(zS

.

The input signal used for modelling )(

ˆ

ns is the

random noise )(nr .

The error signal at quiet zone is expressed as:

)()()()()()( nrnsnynsndne ∗−∗−=

)´()´()( nrnynd −−=

(18)

IMPROVED STABLE FEEDBACK ANC SYSTEM WITH DYNAMIC SECONDARY PATH MODELING

195

Where )(ny

′

is the secondary noise component

due to the original noise and )(nr

′

is the secondary

noise component due to the additive random noise.

An estimate of )(nr

′

, )(

ˆ

nr

′

, is calculated from

the modelling filter

)(

ˆ

zS

and the signal

)(nr

,

according with the eq. (19):

)()(

ˆ

)(

ˆ

nrnsnr ∗=

′

(19)

Figure 9: Feedback ANC system with on-line secondary-

path modelling

Assuming that

)(

ˆ

zS

is a good approximation,

that is

)()(

ˆ

zSzS ≈

, we have

)()(

ˆ

nrnr

′

≈

′

and the

)(ne

′

signal is given by:

)(

ˆ

)()()()( nrnrnyndne

′

+

′

−

′

−=

′

)()( nynd

′

−≈

(20)

At the same time, we get the estimated filtered

control signal )(

ˆ

ny

′

from

)(

ˆ

zS

and )(ny :

)()()(

ˆ

)(

ˆ

nynynsny

′

≈∗=

′

(21)

Finally, we generate the internal reference signal

(estimated signal) )(

ˆ

nx adding the estimated

filtered control signal )(

ˆ

ny

′

to )(ne

′

, according

with the eq. (22):

)(

ˆ

)(

ˆ

)()(

ˆ

ndnynenx =

′

+

′

=

(22)

This last signal is processing with the NFXLMS-

NA algorithm (next section) in order to update the

coefficients of the adaptive filter

)(zW

.

2.6 The NFXLMS-NA Algorithm

Since the control signal )(ny is feedback internally

(in the system) across the estimated secondary path

in order to generated the estimated reference signal

)(

ˆ

nx , and because )(ns could have error in its

estimation, the system could be unstable. In (Rafaely

and Elliot, 1996), it is showed that

“an adaptive

controller can be made robustly stable by an

appropriated level of stabilising noise”

. In that

article, the stabilising

noise is added to the filtered

estimated reference signal )(

ˆ

nx

′

before those

signals cross the )(

ˆ

ns filter. In the paper, some

results of this technique with a fixed secondary path

are showed (Bustamante and Perez, 2002),

(Bustamante et al., 2003).

Instead of that and according with our

development, we (a) added the random noise

)(nr

to the filtered estimated reference signal )(

ˆ

nx

′

before the updated of the coefficients of the adaptive

filter )(nw and (b) the coefficients of the secondary

path are updated dynamically (on-line secondary

path modelling) in a real environment; Fig. 10 shows

this process.

With these changes, we propose the NFXLMS

algorithm with Noise Addition (NFXLMS-NA); the

recursive equation of the NFXLMS-NA algorithm is

derivate using eq. (17) and Fig. 10:

)(

2

)()(

ˆ

)]()(

ˆ

[

)()1( ne

nrnxa

nrnx

nn

GG

G

G

GG

+

′

+

+

′

+=+

ψ

ωω

(23)

Figure 10: Feedback ANC system NFXLMS-NA based

In section 4 are showed the results of the

NFXLMS-NA algorithm.

3 IMPLEMENTATION

Practical feedback ANC system (NFXLMS-NA

based) was implemented using the TMS320C30

evaluation module (EVM) from TI. Characteristics

of the implemented system are the following:

a) The secondary path

)(zS

was an open

environment and it was estimated using the NLMS

algorithm with 500 coefficients.

b) The adaptive filter

)(zW

was estimated using

the NFXLMS-NA algorithm with 500 coefficients

c) The white noise

)(nr

used had an effective

value of 100 milivolts (Vrms).

d) The sampling frequency of the A/D had a

1milisecond period.

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196

e) Different tonal signal between 150 y 500 Hz,

with

f∆

equal to 50 Hz, was used as noise

Fig. 11 illustrates the block diagram of the ANC

system (NFXLMS-NA based); Fig. 12(a) show the

practical scheme and Fig. 12(b) show the DSP board

and part of the equipment used in the

implementation.

In order to have an efficient implementation, we

used assembler language for C30 DSP in the

development of the program; in Fig. 13 is showed

the structure of the main program.

Figure 11: block diagram of the implemented ANC system

12 (a)

12 (b)

Figure 12: (a) Practical scheme and (b) DSP board and

equipment utilized in the implementation

.

Figure 13: Structure of the main program

4 TEST AND RESULTS

In this section, we present some results from

different tests carried out in our feedback ANC

system, with the characteristics explained in the

precedent section. All tests were carried out with

narrow band noise and they were grouped in two

types:

(a) Performance of the NFXLMS-NA algorithm,

from 150 to 550 Hz, at 15 seconds (Fig. 14). In the

figure, upper line shows the original noise; bottom

line shows the attenuated noise.

(b) Cancellation at select frequencies, from 0 to

15 seconds (Fig. 15(a), (b) and (c)).

Figure 16 shows the frequency view of the

cancellation of the (175 Hz + 275 Hz) signal

For Figs 15(a), (b) and (c), the horizontal axis

are values of 100 averaged samples (125

microseconds sample rate) for a total of 15 seconds.

The vertical axis is the amplitude expressed in

decibels (dB´s).

IMPROVED STABLE FEEDBACK ANC SYSTEM WITH DYNAMIC SECONDARY PATH MODELING

197

Figure 14: Performance of the NFXLMS-NA algorithm

Figure 15(a)

Figure 15(b)

Figure 15(c)

Figure 15: Cancellation at select frequencies (a) 200 Hz,

(b) 350 Hz and (c) 175 Hz + 275 Hz

Figure 16: Cancellation at frequencies 175 Hz + 275 Hz

(frequency. view, second 15)

5 CONCLUDING REMARKS

We proposed a new algorithm (NFXLMS-NA) in

order to get a better stability than the FXLMS

algorithm for ANC feedback systems. Experimental

results show that this the proposed ANC feedback

system attenuates narrow band noise just like a

feedforward system; however, this system has not

problem with acoustic feedback, because it works

without a external reference signal. Also, dynamic

tests showed that the on-line modeling of the

secondary path is a source of instability; but the

noise addition in the system makes it stable (the time

for all test were 60 seconds; here, 15 seconds test are

showed).

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198

Finally, in Figs 14 and 15 we can see that some

of the most relevant results are: (a) the system has a

good performance besides the on-line modeling, (b)

narrow band noise is attenuated at least 7 dB´s in

open environments, (c) the system is stable and (d)

decorrelated broadband signals could be recovered

from narrow band noise; this last result was recorded

in an acoustic form.

REFERENCES

Bernard Widrow, J. Glover, J. McCool, Adaptive Noise

Cancelling: Principles and Applications, Proceedings

of IEEE, vol. 63, no 12, pp 1692-1716, Dec. 1975.

S. Kuo and D. Morgan, Active Noise Control Systems:

Algorithms and DSP implementations, New York,

N.Y.: John Wiley, 1996.

Stephen Elliot, Signal Processing for Active Control,

Academic Press, 2001.

B. Farhang-Boroujeny, Adaptive Filters: Theory and

Applications (Baffins Lane,Chichester: John Wiley,

1998)

S. Haykin, Adaptive Filter Theory, Upper Saddle River,

New Jersey: Prentice Hall, 1996 .

Victor Solo, Xuan Kong, Adaptive Signal Processing

Algorithms: Stability and Performance, Englewood

Cliffs, New Jersey, 1995.

Bustamante, R., H. M. Perez, Development and

Simulation of Active Noise Control Systems,

Proceedings of the 2002 International Symposium on

Active Control of Sound and Vibration, Southampton,

U.K., July 2002, pp 793-802.

Bustamante, R., H. M. Perez-Meana, and B. Psenicka,

Development, Simulation and Comparison of

Orhtogonalized LMS Algorithms for Active Noise

Control, in the International Technological Journal

Electromagnetic Waves and Electronic Systems,

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