Implementations of arbitrarily fast adaptive lattice filters with multiple slow processing elements

This paper describes systolic realizations of adaptive lattice filters with arbitrarily high sampling rates using relatively slow processing elements. The lattice filter is a desirable structure for this purpose because it can adapt coefficients within each stage using the residual errors from the previous stage and the adaptation algorithms at each stage can be modelled as time-varying linear systems. The properties of independence among stages and linear state-updates make adaptive lattice filters suitable for implementations with arbitrary levels of concurrency. The architecture introduced can be called the vectorized adaptive lattice filter with parallel input and output. It has the property that an arbitrarily high sampling rate can be achieved at the expense of latency. An example of vectorized adaptive lattice filters, the implementation of a normalized prewindowed least-squares lattice predictor, is illustrated, and its latency and complexity are discussed.