Small side-lobe channel-banks suitable for multi-tone data-communications

An approach for realizing filter-banks having improved side-lobe performance compared to approaches based on inverse-Fourier-transforms (IFTs), especially for greater frequency differences from the pass-band 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 a constraint added that results in significantly improved stop-band performance. The proposed channel-banks are suitable for realizing multi-tone digital data-communication systems, such as asymmetric-digital-subscriber-line (ADSL) systems. Better stop-band performance has been shown in a previous approach, based on the use of wavelet transforms, to affect improved performance of ADSL systems. The filters reported here offer further improved stop-band performance compared to those reported previously for similar orders. Under the conditions of maximal decimation, the reconstruction is not perfect, but aliasing errors are small-enough to be negligible in most practical communication systems. For some cases, the filter coefficients can be calculated exactly without using optimization. For other cases, a single simplified optimization suffices independent of the filter order