A windowing approach for designing critically sampled nearly perfect-reconstruction cosine-modulated transmultiplexers and filter banks

A very fast technique for designing nearly perfect-reconstruction (NPR) critically sampled cosine-modulated M-channel transmultiplexer (TMUX) and filter bank (FB) systems is proposed. This technique is based on using the windowing technique for designing the prototype filter so that its 3-dB cutoff frequency is located at ω=π/(2M). The motivation for this is the observation that if the prototype filter cascaded with itself is a 2Mth filter, then the resulting TMUX (in the case of an ideal channel being a pure delay) or FB system has approximately a perfect-reconstruction (PR) property. This implies that for this cascade the 6-dB cutoff point should be approximately located at ω=π/(2M), and, correspondingly, the 3-dB cutoff frequency of the prototype filter is located at this angular frequency. The main advantage of the proposed design scheme is that it significantly lowers the computational complexity when compared with other existing techniques proposed for designing critically sampled cosine-modulated TMUX or FB systems. The PR property is not achieved, but for the resulting TMUX (FB) systems, the intersymbol interference and crosstalk errors (the amplitude and alias errors) are small. Both of these errors are small enough in practical systems. Several examples are included illustrating these desired properties.