Title :
Derivation of the Class of Digital Filters With All Second-Order Modes Equal
Author :
Yamaki, Shunsuke ; Abe, Masahide ; Kawamata, Masayuki
Author_Institution :
Dept. of Electron. Eng., Tohoku Univ., Sendai, Japan
Abstract :
This paper reveals the class of digital filters with all second-order modes equal. We first prove that if the second-order modes of a digital filter are all equal, the L2-sensitivity minimization problem of the digital filter can be solved analytically. We derive a general expression of the transfer function of digital filters with all second-order modes equal. Furthermore, we show that the general expression is obtained by a frequency transformation on a first-order prototype FIR digital filter.
Keywords :
FIR filters; transfer functions; all second-order modes equal; first-order prototype FIR digital filter; frequency transformation; transfer function; Controllability; Eigenvalues and eigenfunctions; Genetic expression; Minimization; Observability; Optimized production technology; Transfer functions; Analytical solutions\´ $L_{2}$-sensitivity minimization; first-order FIR digital filters; frequency transformations; second-order modes; state-space digital filters;
Journal_Title :
Signal Processing, IEEE Transactions on
DOI :
10.1109/TSP.2011.2164403
