Lattice filter with adjustable gains and its application in optical signal processing

In this paper, we consider a class of N-th order lattice filter with gains as an extension to the traditional lattice filter structures and develop analysis and synthesis of such filters. In the analysis-synthesis parts, we present recursive methods to derive the input-output transfer function of the filter in terms of parameters of the lattice structure such as the time delay, gains, transmission and reflection coefficients and vice versa. Stability of the filter is analyzed and an algorithm to test the stability is proposed. This class of MIMO lattice filters with adjustable gains models integrated photonic devices under development in our labs for optical communication and high speed signal processing applications. Our signal processing approach to characterizing this type of lattice structures can also be used in filter realization by VLSI, FPGA, or programmable processors for acoustic or speech applications