In this paper, we define a concept of signal matched multirate whitening filter bank which provides an optimum coding gain. This is achieved by whitening the outputs, of the analysis filter bank, within as well as across the channels, by solving a constrained projection problem. We also present a fast time and order recursive least squares algorithm to obtain the vector output of the proposed analysis filter bank. The recursive algorithm, developed here, gives rise to a lattice-like structure. Since the proposed signal matched analysis filter bank coefficients are not available directly, an order recursive algorithm is also presented for estimating these from the lattice parameters. Simulation results are presented to validate the theory. It is also observed that the proposed algorithm can be used to whiten Gaussian/non-Gaussian processes with minimum as well as non-minimum phase.