Approximating lapped transforms through unitary postprocessing

We deal with the approximation of a nonsquare lapped transform matrix by another matrix. This second matrix is constrained to be the product of two stages: one lapped transform and a unitary postprocessing step, in such a way that approximation is accomplished by modifying the postprocessing stage alone. Viewing both matrices as transforms, the goal is to minimize the variance of the output error (discrepancy) for given input signal statistics. An extension of the result to frequency responses of filter bank transfer matrices is also given along with an example to demonstrate the feasibility of the method. The example demonstrates the potential use of the method in modifying transforms which can be applied in audio compression.