Parametrization of filters on the basis of orthonormal basis functions have been widely used in system identification and adaptive signal processing. The main advantage of using orthonormal basis functions for a filter parametrization lies in the possibility of incorporating prior knowledge of the system dynamics into the identification process and adaptive signal process. As a result, a more accurate and simplified filter with less parameters can be obtained. In this paper, several construction methods of orthonormal basis function are discussed and analyzed. An application of active noise control based on these orthonormal basis constructions is presented.

1.
Heuberger
P. S. C.
,
Van Den Hof
P. M. J.
, and
Bosgra
O. H.
,
1995
. “
A generalized orthonormal basis for linear dynamical systems
.”
IEEE Transactions on Automatic Control
,
40
(
3
), pp.
451
465
.
2.
Ninness
B.
, and
Guslafsson
R
,
1997
. “
A unifying construction of orthononrial bases for system identification
.”
IEEE Transactions on Automatic Control
,
42
(
4
), pp.
515
521
An extended version is available as Technical report EE9433, Department of Electrical and Computer Engineering, University of Newcastle, Australia, 1994.
3.
de Vries
D. K.
, and
Van Den Hof
P. M. J.
,
1998
, “
Frequency domain identification with generalized orthonormal basis functions
.”
IEEE Transactions on Automatic Control
,
43
(
5
). pp.
656
669
.
4.
Ninness
B.
,
Hjalmarsson
H.
, and
Gustafsson
F.
,
1999
. “
The fundamental role of generalized orthonormal basis in system identification
.”
IEEE Transactions on Automatic Control
,
44
(
7
), pp.
1384
1406
.
5.
Szabo´
Z.
,
Heuberger
P. S. C.
,
Bokor
J.
, and
Van Den Hof
P. M. J.
,
2000
. “
Extended Ho-Kalman algorithm for systems represented in generalized orthonormal bases
.”
Automatica
,
36
, pp.
1809
1818
.
6.
de Hoog
T. J.
,
Szabo´
Z.
,
Heuberger
P. S. C.
,
Van Den Hof
P. M. J.
, and
Bokor
J.
,
2002
. “
Minimal partial realization from generalized orthonormal basis function expansions
.”
Automatica
,
38
, pp.
655
669
.
7.
Heuberger
P. S. C.
,
De Hoog
T. J.
,
Van Den Hof
P. M. J.
, and
Wahlberg
B.
,
2003
. “
Orthonormal basis functions in time and frequency domain: Hambo transform theory
.”
SIAM Journal on Control & Optimization
,
42
(
4
), pp.
1347
1373
.
8.
Wahlberg
B.
,
1991
. “
System identification using laguerre models
,”
IEEE Transactions on Automatic Control
,
AC–36
, pp.
551
562
.
9.
Wahlberg
B.
,
1994
. “
System identification using kautz models
.”
IEEE Transactions on Automatic Control
,
AC–39
, pp.
1276
1282
.
10.
Zeng, J., and de Callafon, R. A., 2005. “Generalized FIR filters for adaptive filtering with application to active noise control.” Submitted for publication in IEEE Trans. on Industry Applications.
11.
Kuo, S. M., and Morgan, D. R., 1996. Active Noise Control Systems - Algorithms and DSP Implementations. John Wiley and Sons Inc.
12.
Fuller
C. R.
, and
Von Flotow
A. H.
,
1995
. “
Active control of sound and vibration
.”
IEEE Control Systems Magazine
,
15
(
6
), pp.
9
19
.
13.
Berkman
E. F.
, and
Bender
E. K.
,
1997
. “
Perspectives on active noise and vibration control
.”
Sound and Vibration
,
31
, pp.
80
94
.
14.
Cabeli
R. H.
, and
Fuller
C. R.
,
1999
. “
A principal component algorithm for feedforward active noise and vibration control
.”
Journal of Sound and Vibration
,
227
, pp.
159
181
.
15.
Ha¨nsler, E., and Schmidt, G., 2004. Acoustic Echo and Noise Control: A Practical Approach. John Wiley & Sons, Hoboken, New Jersey.
16.
Denenberg
J. N.
,
1992
. “
Anti-noise
.”
IEEE Potentials
,
11
, pp.
36
40
.
17.
Wang
C. N.
,
Tse
C. C.
, and
Wen
C. W.
,
1997
. “
A study of active noise cancellation in ducts
.”
Mechanical Systems and Signal Processing
.
11
(
6
), pp.
779
790
.
18.
Ljung, L., 1999. System Identification: Theory for the User. Prentice Hall.
19.
Landau, I. D., 1990. System Identification and Control Design: Using P. I. M. Plus Software. Prentice Hall.
This content is only available via PDF.
You do not currently have access to this content.