Transient and convergent behavior of the adaptive line enhancer

The adaptive line enhancer (ALE) was first described as a practical technique for separating the periodic from the broad-band components of an input signal and for detecting the presence of a sinusoid in white noise. Subsequent work has shown that this adaptive filtering structure is applicable to spectral estimation, predictive deconvolution, speech processing, interference rejection, and other applications which have historically used matrix inversion or Levinson's algorithm techniques. This paper uses an eigenvalue-eigenvector analysis of the expected ALE impulse response vector to demonstrate properties of the convergent filter and to quantify the convergence time and characteristics of the ALE. In particular the ALE's response to a sinusoid plus white noise input is derived and compared to a computer simulation of the ALE with such an input. The eigenvalue-eigenvector technique is then used to evaluate the ALE's performance as an adaptive prewhitener for autoregressive (AR) models with white observation noise. A method is demonstrated which prevents the problem of spectral estimation bias which usually accrues from the observation noise.