On the frequency domain LMS adaptive line enhancer

The theory for a computationally efficient, frequency domain adaptive line enhancer (ALE) structure, which uses the N-point DFT (discrete Fourier transform) for N-point input data blocks, is extended. It is shown that unless the input block covers an integer number of cycles, the SNR (signal/noise ratio) gain of this structure is lower than that of a time-domain ALE with the same number of taps. Analytical results for an ALE with a sinusoidal input indicate that independent weight updating in the discrete frequency domain is far from being optimum, unless the frequencies coincide, which is extremely improbable. The optimum solution is shown to be a matrix transformation on the input. The authors also propose a suboptimum structure that improves the performance over the independent-weight-updating scheme.