Efficient linear-phase directional filters with selectable centre frequencies

We consider complex-valued digital directional filters that extract two freely selectable user signals from an FDM signal, which comprises up to four independent user spectra uniformly allocated along the frequency axis from zero frequency up to the sampling rate. Two different approaches, both applying linear-phase FIR halfband filters, are investigated and compared with each other in terms of computational efficiency. The first approach is based on a complex-modulated frequency demultiplexer filter bank (FDMUX); it requires the least number of delay elements. The second approach combines two complex offset halfband filters (COHBF) that allow for the exploitation of coefficient symmetry; hence, the computation required is minimal. Finally, the dual directional filter effectuating frequency multiplexing is derived by transposition of the FDMUX and COHBF approaches.