Title :
A frequency-domain approach to frequency-weighted balanced realization
Author_Institution :
Dept. of Electron., Macquarie Univ., Sydney, NSW, Australia
fDate :
5/1/2003 12:00:00 AM
Abstract :
The Ho-Kalman/Kung algorithm for balanced realization by singular-value decomposition of the Hankel operator has a natural frequency-domain equivalent. The controllability operator and observability operator are represented by intermediate transfer functions, called the gain to states and noise gain respectively. The product of these, the Hankel operator, can be expressed in terms of the input-output transfer function using an identity which the author refers to as the dynamic-range limitation. This frequency-domain theory extends naturally to the frequency-weighted case, and further to non-integrator-based linear fractional systems. It also provides additional design insight into the filter dynamic-range problem.
Keywords :
Hankel matrices; Laplace transforms; active filters; controllability; frequency response; frequency-domain analysis; low-pass filters; observability; singular value decomposition; state-space methods; transfer functions; Hankel operator; Ho-Kalman/Kung algorithm; Laplace transformation; controllability operator; dynamic-range limitation; filter dynamic-range problem; frequency-domain approach; frequency-weighted balanced realization; gain to states; input-output transfer function; intermediate transfer functions; low-pass filter; noise gain; nonintegrator-based linear fractional systems; observability operator; singular-value decomposition; state-space realization algorithm; Active filters; Controllability; Digital filters; Filtering theory; Frequency domain analysis; Kalman filters; Matrix decomposition; Observability; Time domain analysis; Transfer functions;
Journal_Title :
Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on
DOI :
10.1109/TCSI.2003.811021
