Oversampled DFT-Modulated Biorthogonal Filter Banks: Perfect Reconstruction Designs and Multiplierless Approximations

Abstract

We propose a novel methodology for designing oversampled discrete Fourier transform-modulated uniform filter banks. The analysis prototype is designed as a Nyquist filter, whereas the synthesis prototype is designed to guarantee perfect reconstruction (PR) considering oversampling. The resulting optimization problem fits into the disciplined convex programming framework, as long as some convex objective function is employed, as the minimization of either the stop-band energy or the maximum deviation from a desired response. The methodology also accounts for near-PR multiplierless approximations of the prototype analysis and synthesis filters, whose coefficients are obtained in the sum-of-power-of-two (SOPOT) space. The quantized coefficients are computed using successive approximation of vectors, which is able to yield filters with a reduced number of SOPOT coefficients in a computationally efficient manner. The proposed methodology is especially appealing for supporting actual hardware deployments, such as modern digital transparent processors to be used in next-generation satellite payloads.