Design of perfect reconstruction FIR filter banks using DFT modulation

In this paper, we present a method for designing perfect reconstruction (PR) FIR filter banks by discrete Fourier transform modulation (DFT modulation). In previous work, cosine-modulated PR filter banks were shown to be easy to design and capable of fast processing. But this method is inconvenient because of its restriction of filter length. In our new approach, filter banks are implemented by DFT modulation of the prototype filter with complex coefficients, yielding some advantages over the previous work. Our proposed filter banks are a new formulation of modulated filter bank design and an alternative implementation of cosine-modulated filter banks. We propose an optimization technique using the Lagrange-Newton method. The effectiveness of the proposed method is demonstrated with design examples.