utput Statistics of the

Abstmc#-The adaptive line enhancer (ALE) is an adaptive digital a deterministic sinusoid in white Gaussian noise is worked out filter designed to suppress uncorrelated components of its input, while passing any narrow-band components with little attenuation. The purpose of this paper is to analyze the second-order output statistics of as an example. Finally, a number of applications for these results are described. the ALE in steady-state operation, for input samples consisting of weak narrow-band signals in white Gaussian noise. The ALE output is shown to be the sum of two uncorrelated components, one arising from opti-11. BASIC PROPERTIES OF THE ALE The block diagram of Fig. I reveals the ALE to be a particumum finite-lag Wiener filtering of the narrow-band input components, and the other arising from the misadjustment error associated with the adaptation process. General expressions are given for the output autocorrelation function and power spectrum with arbitrary narrow-band input signals, and the case of a single sinusoid in white noise is worked lar variation of an LMS adaptive filter [5], wherein the ‘‘reference” or “desired ” response is merely the current input x(k) and the “primary ” input is a delayed version of x@). The input x(k) is assumed to be of the form out as an example. Finally, the significance of these results to practical applications of the ALE is mentioned. x(k) = s(k) + n(k) (1) I