Existence of unique solutions for multirate FIR filters based on Lagrange multipliers
G.W. Medlin, John W. Adams, Cornelius T. Leondes · 2003
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.>