% MATLAB code for paper:
%
% Ha T. Nguyen and Minh N. Do, Hybrid Filter Banks With Fractional Delays:
% Minimax Design and Applications to Multichannel Sampling, IEEE
% Transactions on Signal Processing, vol. 56, no 7, July 2008.
%
% Last modification date: December 15th, 2008.
% Upload date December 15th, 2008.
%
% Created by Ha Nguyen (Sony Electronics Inc.)
%
% DEMO:
% demo: demo of the design procedure and plots of figures shown in
% the paper
%
% Main functions:
% designIIR: design filters F_i(z) (as in Section III.B.)
% designFIR: design filters F_i(z) (as in Section IV.B.)
%
% Other functions used in demo, designIIR and designFIR:
% initialization
%
% analog_conv: simulate an analog system. Input and output will be
% given as an array of values at equi-distance time interval.
%
% plot_equi_filters: plot Fig. 12 in the paper.
%
% getAd: get the A-matrix as in equation (15)
% getBd: get the B-matrix as in equation (16) and Lemma 2
% getCd: get the C-matrix as in equation (15)
%
% getF: get the IIR filters F_1(z),..., F_N(z) from the system F
% getH: get system H as in Theorem 1
% getP: get system P as in Figure 7
% getW: get system W as in Theorem 1
%
% INTDELAYOP: Integer Delay Operator. IntDelayOp delays the i-th
% channel of a digital LTI system by m(i) samples.
%
% Analog2Digital: bilinear transformation of an analog system K to
% discrete time
%
% Digital2Analog: bilinear transformation of a discrete system P to
% analog domain
%
% LMI_OPT: Linear Matrix Inequality Optimization, used in the design
% of FIR filters F_i(z), as described in Section IV.B.
%
% MVL: compute the integral Mij(t) as in equation (51)