Design of Multiple Order Allpass Transformed DFT Filter-Banks with Aliasing-Free Signal Reconstruction by Linear Programming

The allpass transformation of multiple order is a very general approach to design a frequency warped analysis-synthesis filter-bank (AS FB) with non-uniform time-frequency resolution. In the design process, the delay elements of the analysis filter-bank are substituted by allpass filters of higher order to achieve a very flexible control over its frequency selectivity. Analytical closed-form designs for the synthesis filter-bank can ensure perfect reconstruction (PR), but the synthesis subband filters are not necessarily stable or exhibit a bandpass characteristic. We tackle these problems by a constrained least-squares error (CLS) design. The coefficients of the new synthesis filter-bank are determined by a linear set of equations with linear constraints. The resulting synthesis filters are stable and exhibit a distinctive bandpass characteristic. Our design by linear programming can achieve an aliasing-free, near-perfect signal reconstruction, where the signal delay is an adjustable design parameter. These properties make the proposed filter-bank of interest for subband processing systems requiring non-uniform frequency bands.