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International Journal of Engineering Research and Development e-ISSN: 2278-067X, p-ISSN : 2278-800X, www.ijerd.com
Volume 5, Issue 2 (December 2012), PP. 44-46

System Identification-Different Techniques
Ramesh Kr1, Chitranjan Kr2, Ruchita3
1

National Institute of Technology Patna, 2PSCET Vaishali, 3RIET Jaipur

Abstract:- Engineering applications require description of the dynamic behavior of the system. Though a no. of applications are known in the field of system identification, three techniques are considered for the identification of linear system. Different techniques are frequency chirp, coherence function and pseudoinverse. In chirp method, wideband excitation such as frequency chirp is used. Frequency response is …show more content…

System Identification by inverse filtering requires computation of the (pseudo)inverse of X(z). If the system is assumed casual, then the form of the (p+1)×(s+1) matrix is :

44

System Identification-Different Techniques
 x(0)
0

.

X  .
.

0
0


x(1)

x(2)

..

x( s  1)

x(0)

x(1)

..

x( s  2)

.

.

..

.

.

.

..

.

.

.

..

.

0

0

..

x(0)

0

0

..

0

x( s )

x( s  1) 


.

.


.

x( s  p  1)  x( s  p) 


where the output sequence has s+1 samples and the impulse response is estimated at p+1 points with p = s.
C. Coherence
For a linear system, the coherence function is given as

Cxy ( k ) 

Sxy ( k )
Sxx ( k ) Syy ( k )

(2)

where Sxy (ωk) is the input-output cross-spectrum (i.e., the power spectrum of the cross-correlation between the input and output functions), and Sxx (ωk) and Syy (ωk) are the power spectra of the autocorrelations of the input and output, respectively. The function C2xy (ωk) can be interpreted as the fraction of the mean square value of y(n) that can be attributed to the component of the input x(n) at frequency ωk . Usually, pseudorandom noise is used as an input x(n). The two identification methods, direct and inverse, then estimate the system response as

Sxy ( k )
Sxx ( k )
Syy ( k )
H 2( k ) 
Sxy ( k )
H 1( k ) 

(3)

where H1(  k ) tends to

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