A systematic technique for designing linear-phase FIR prototype filters for perfect-reconstruction cosine-modulated and modified DFT filterbanks

This paper describes a systematic technique for designing prototype filters for generating perfect-reconstruction (PR) orthogonal cosine-modulated and modified discrete Fourier transform filterbanks. In the proposed design scheme, the stopband energy of the prototype filter is minimized, and the basic unknowns are the angles of a special lattice structure used for implementing the prototype filter so that the PR property is automatically satisfied independent of the angle values. This selection of the unknowns makes the overall optimization problem unconstrained. Due to the fact that there are several local optima, the design is performed in multiple steps in order to arrive at least at a very good suboptimal solution. First, for the given number of channels, the length of the channel filters, and the stopband edge of the prototype filter, the corresponding two-channel filterbank is designed based on the preoptimized data. Then, after knowing the angles for the optimized two-channel case, the prototype filter for the desired filterbank is generated by gradually increasing the number of channels and by properly using the result of the previous step as a start-up solution for the present step. The main benefit of the proposed design technique is that it enables one to effectively design prototype filters for filterbanks with very high-order analysis and synthesis filters.