Review of Cosine Sum Window Functions and Recent Advances in FIR Filter Design Methods

novel efficient and enhanced combinational window family is proposed for developing the prototype filter for a two-channel quadrature mirror filter bank, where the gradient-based optimization technique is employed to minimize the distortions in amplitude. The filter bank design issue is formulated to build a low pass prototype filter with optimum responses in passband and stopband region, with filter coefficient at quadrature frequency ( π /2) being (1/√(2)) . The prototype filter is designed with the proposed combinational window function, whose frequency at cut-off is altered iteratively by a gradient-based optimization algorithm. Upon realization of convergence, the reconstruction error in the analysis filter bank is minimized. The proposed design significantly reduces peak reconstruction error with better tail-end attenuation when compared with other existing combinational windows along with reduction in computational time. The results of several design examples have been simulated, and they validate the improved and efficient design of the proposed window design over other combinational windows optimized with the computationally efficient proposed algorithm.