Optimized transmultiplexers for multirate systems

A very fast filter bank optimization technique is proposed for synthesizing efficient nearly perfect-reconstruction cosine-modulated transmultiplexer systems for multicarrier modulation. The most important problems in communications systems are the existence of both the ISI and inter-carrier interference. In order to properly minimize both of these, a windowing technique is used for generating the prototype filter for the cosine-modulated synthesis and analysis filter banks in such a way that a proper weighted sum of the above-mentioned interferences in the sub-channels is minimized. For this purpose, the parameters of the generalized Blackman window proposed by the authors of this paper and the cutoff frequency of the ideal filter are optimized subject to the condition that the 3-dB cutoff frequency of the prototype filter occurs at ω=π/(2M) with M being the number of channels. Numerical simulations show that the proposed technique leads to an increase in the signal-to-interference ratio compared to the original Blackman window giving the best results, according to our experience, among the well-known windows.