Title :
Eigenvalues of a matrix inside an ellipse and Chebyshev filter
Author_Institution :
General Dynamics, San Diego, CA, USA
fDate :
12/1/1979 12:00:00 AM
Abstract :
The conditions for a matrix to have all its eigenvalues inside an ellipse are obtained and explained in terms of a vector norm. A set of functions orthogonal on the ellipse is obtained and the relation between the Chebyshev filter and these functions is presented. The Butterworth filter is derived as a particular case.
Keywords :
Chebyshev filters; Eigenvalues; Matrices; Orthogonal functions; Chebyshev approximation; Difference equations; Eigenvalues and eigenfunctions; Finite impulse response filter; IEL; Identity-based encryption; Polynomials; Robustness; Stability;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.1979.1102204
