Small side-lobe filter design for multitone data-communication applications

An approach for realizing filter banks having improved side-lobe performance compared to approaches such as those based on inverse Fourier transforms (IFTs), especially for greater frequency differences from the passband frequencies, is presented. The approach is based on using a weighted-sum of near-adjacent IFT filters to realize the individual channel-bank filters, but with constraints added that results in significantly improved stopband performance while still achieving small reconstruction errors. The proposed channel banks are suitable for realizing multitone digital data communication systems, such as Asymmetric Digital Subscriber Line (ADSL) systems, where stopband performance is critical. Under the conditions of maximal decimation, the reconstruction is not perfect, but aliasing errors are small enough to be negligible in practical communication systems. For some cases, the filter coefficients can be determined exactly without using optimization. Given the frequency-weighting coefficients reported herein, near-optimal multirate filter banks may be designed exactly without optimization for all even n