Special properties of the modified DFT to achieve algorithmic fault tolerance in Adaptive Filters

Previously published results showed that when an FFT-based transform domain Fault Tolerant Adaptive Filter (FTAF) operates on real-valued signals, parameter redundancy inherent in the complex arithmetic provides fault tolerant capabilities. It was shown experimentally that the Modified Discrete Fourier Transform (MFFT) generates frequency domain samples that are not strictly real-valued or constrained to have conjugate symmetry in the transform domain. This paper provides a more detailed analysis of the fault tolerant capabilities of MFFT-FTAF architectures and further demonstrates how the MFFT-FTAF architecture is able to overcome certain fault conditions that cannot be properly handled in a conventional FFT-based FTAF architecture.