  In the companion paper, we proposed a concept of signal matched whitening
filter bank and developed a time and order recursive, fast least squares
algorithm for the same. Objective of part II of the paper is two fold: first is
to define a concept of signal matched synthesis filter bank, hence combining
definitions of part I and part II we obtain a filter bank matched to a given
signal. We also develop a fast time and order recursive, least squares
algorithm for obtaining the same. The synthesis filters, obtained here,
reconstruct the given signal only and not every signal from the finite energy
signal space (i.e. belonging to L^2(R)), as is usually done. The recursions, so
obtained, result in a lattice-like structure. Since the filter parameters are
not directly available, we also present an order recursive algorithm for the
computation of signal matched synthesis filter bank coefficients from the
lattice parameters. The second objective is to explore the possibility of using
synthesis side for modeling of a given stochastic process. Simulation results
have also been presented to validate the theory.
