Exponentially-modulated filter bank-based transmultiplexer

A complex filter bank divides the spectrum of a complex (I/Q) signal into several low-rate subbands (analysis bank) or combines the low-rate signals into a single high-rate signal (synthesis bank). These operations are often cascaded to form analysis-synthesis (AS) or transmultiplexer (TMUX) configurations. Such systems find applications in many areas, especially in communications signal processing. In this paper we develop further the lapped transform theory to cover also the cases of complex, exponentially modulated filter banks. Using the shift-orthogonality of lapped transforms, we show how to design complex critically sampled AS and TMUX systems such that the perfect-reconstruction condition is satisfied.