Second-order output statistics of the adaptive line enhancer

Adaptive enhancement of finite bandwidth signals in white Gaussian noise

“…This implementation is the adaptive line enhancer (ALE) which is discussed in references [1, 10,[25][26][27][28][29][30][31][32][33].…”

“…The gain in output SNR of the ALE relative to that of the input was shown to be dependent on the input SNR and is limited by the algorithm noise of the LMS estimation algorithm [26]. It was demonstrated in [291 that the statistical properties of the input are significantly altered by the ALE.…”

A Determination of the First Two Moments of the Ale Output Detector.

“…Let K be the DFT length in the ALE output detector pictured in figure 2 and assume that max (2K , K + L) << r. Then a single output of the detector, y, with no averaging has mean [11 (5 1)…”

Frequency-response-shaped LMS adaptive filter

“…A simplified expression can be obtained for the gain at frequencies that are multiples of π/N [10] as…”