Synthesis of bandwidth efficient OQAM and VSB transmultiplexers

A set of conditions which allow bandwidth efficient transmultiplexers to be synthesized is developed. The synthesis procedure is based on a generalized impulse response for the combining (modulating) and separation (demodulating) filters. In particular, the combining and separation filters are bandpass versions of one or two lowpass prototypes and are configured to cancel crosstalk by exploiting relationships between the center frequencies, delays, and phases in their impulse response. Based on the derived conditions, five different transmultiplexers are synthesized. Three of them implement orthogonal quadrature amplitude modulation (OQAM) with repeated center frequencies. The other two accomplish vestigial sideband modulation (VSB) with distinct frequencies. The transmultiplexers can be converted into new complementary subband systems. Intersymbol interference is eliminated in both the transmultiplexers and the subband systems by appropriately designing the prototypes