Fault tolerant adaptive filters based on number theoretic transforms

Previously it was shown that FFT-based transform domain adaptive filters operating on real-valued signals can achieve adaptive fault tolerant performance based on parameter redundancy inherent in the complex arithmetic. In this paper the Fermat number transform (FNT) is combined with transform domain block processing as an alternate way of achieving computationally efficient fault tolerance. It is shown that a hybrid combination of Fermat transform domain block processing and polynomial ring theory provides computationally efficient fault tolerance for adaptive filters implemented in highly scaled nano-technology circuits.