Second-order output statistics of the adaptive line enhancer

Abstract

The adaptive line enhancer (ALE) is an adaptive digital 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 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 optimum 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 auto-correlation function and power spectrum with arbitrary narrow-band input signals, and the case of a single sinusoid in white noise is worked out as an example. Finally, the significance of these results to practical applications of the ALE is mentioned.