The uniqueness of the transfer function of linear systems from input-output observations

Metrika ◽  
1984 ◽  
Vol 31 (1) ◽  
pp. 157-181
Author(s):  
M. Deistler ◽  
B. M. Pötscher ◽  
J. Schrader
Keyword(s):  
Transfer Function ◽  
Linear Systems ◽  
Input Output

scholarly journals Determination of positive realizations with reduced numbers of delays or without delays for discrete-time linear systems

2012 ◽  
Vol 22 (4) ◽  
pp. 451-465 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Transfer Function ◽  
Linear Systems ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Diagram Method ◽  
State Variable ◽  
Discrete Time Systems ◽  
Time Systems ◽  
Time Linear

A new modified state variable diagram method is proposed for determination of positive realizations with reduced numbers of delays and without delays of linear discrete-time systems for a given transfer function. Sufficient conditions for the existence of the positive realizations of given proper transfer function are established. It is shown that there exists a positive realization with reduced numbers of delays if there exists a positive realization without delays but with greater dimension. The proposed methods are demonstrated on a numerical example.

Parameter estimation of linear systems with input-output noisy data: A generalized lp norm approach

1994 ◽  
Vol 37 (3) ◽  
pp. 345-356 ◽  
Author(s):  
Jeng-Ming Chen ◽  
Bor-Sen Chen ◽  
Wei-Sheng Chang
Keyword(s):  
Parameter Estimation ◽  
Linear Systems ◽  
Noisy Data ◽  
Input Output ◽  
Lp Norm

A scheme for expressing instrumental responses parametrically

1977 ◽  
Vol 67 (3) ◽  
pp. 957-969 ◽  
Author(s):  
Peter C. Luh
Keyword(s):  
Transfer Function ◽  
Linear Systems ◽  
Hilbert Transform ◽  
Transfer Functions ◽  
Poor Quality ◽  
Phase Response ◽  
Seismic Instrument ◽  
Amplitude Response ◽  
Response Range

abstract This study shows that, provided a seismic instrument as a whole behaves linearly over its response range, and provided its phase response is known accurately, the instrumental responses can be parametrically expressed in terms of transfer functions of linear systems. The scheme is based on the observation that knowing accurately the detailed overall amplitude and phase responses of a linear instrument is tantamount to knowing all the pertinent constants for the construction of its overall transfer function. Because of generally poor quality of empirical phase calibrations, empirical phases are substituted by minimum phases, calculated via a Hilbert transform of amplitude response. Application of the scheme to actual SRO (LP) and USGS (SP) instruments resulted in sufficiently close agreements between parametric and actual responses to warrant the utility of the scheme.

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