Design of periodic window functions in filter window filter banks for harsh environments

This paper proposes the designs of the periodic window functions in the filter window filter banks for harsh environments. Here, two different cases are considered. The first case assumes that the second periodic window functions are constant. The second case assumes that the second periodic window functions are time varying. For the first case, the design of the periodic window functions is formulated as an L0 norm optimization problem. In particular, the total number of the nonzero coefficients of the impulse responses of the periodic windows is minimized subject to the exact perfect reconstruction condition. The solution of this L0 norm optimization problem is found via an orthogonal matching pursuit method. For the second case, the design of these two periodic window functions is also formulated as an L0 norm optimization problem. In particular, the total number of the nonzero coefficients of the impulse responses of these two periodic window functions is minimized subject to the exact perfect reconstruction condition. Likewise, the orthogonal matching pursuit method is employed for finding a solution of the optimization problem. The designed filter window filter banks are employed for harsh environments.