Title :
Existence of unique solutions for multirate FIR filters based on Lagrange multipliers
Author :
Medlin, G.W. ; Adams, J.W. ; Leondes, C.T.
Author_Institution :
Hughes Aircraft Co., Los Angeles, CA, USA
Abstract :
The Lagrange multiplier method is presented for the design of FIR (finite-impulse-response) digital filters for multirate applications. It is shown that under certain conditions, the optimal filter can be obtained as the solution to a linear system of equations which is related to a Vandermonde matrix. As Vandermonde matrices are always nonsingular, the existence and uniqueness of the optimal solution are guaranteed. As an example, optimal lowpass prototype filter for an FFT (fast Fourier transform) filter bank of 64 bandpass channels was designed.<>
Keywords :
digital filters; FFT filter bank; Lagrange multipliers; Vandermonde matrix; digital filters; example; fast Fourier transform; linear system of equations; multirate FIR filters; optimal filter; optimal lowpass prototype filter; optimal solution; unique solutions; Band pass filters; Channel bank filters; Digital filters; Equations; Filter bank; Finite impulse response filter; Lagrangian functions; Linear systems; Nonlinear filters; Prototypes;
Conference_Titel :
Circuits and Systems, 1988., IEEE International Symposium on
Conference_Location :
Espoo, Finland
DOI :
10.1109/ISCAS.1988.15394
