Fault Tolerance in Transform-Domain Adaptive Filters Operating With Real-Valued Signals

Fault-tolerant adaptive filters (FTAFs) rely on inherent learning capabilities of the adaptive process to compensate for transient (soft) or permanent (hard) errors in the hardware implementation. In this paper, the use of the Walsh-Hadamard transform is first analyzed as a computationally efficient way of achieving adaptive fault tolerance, where a zero padding strategy is used to compensate for faulty filter coefficients. It is then shown that a fast-Fourier-transform (FFT)-based transform-domain FTAF operating on real-valued signals can provide a similar degree of fault tolerance without introducing redundancy in the form of zero padding. The complex arithmetic provides inherent fault-tolerant capabilities. This is achieved by using only the real part of the error to drive the coefficient updates. In the case of an N-tap filter, the FFT-based FTAF can protect up to N-2 filter coefficients.