Adaptive line enhancer used for spectral resolution. ALE resolution of two sinusoids in the presence of white noise is determined for various filter and signal parameters

ALE spectral resolution was analyzed by using the solutions for the converged ALE weight vector. The functions abs. val. (H(Omega)), Q(Omega), and S(Omega) each contain information pertaining to spectral resolution. When the bulk delay, Delta, is greater than 1, both abs. val. (H(Omega)) and S(Omega) experience more than one resolved-unresolved transition as the frequency separation between two sinusoids is decreased. This phenomemon is completely explained by the basic weight vector solution. By Marple's criterion, the resolutions of abs. val. (H(Omega)) and Q(Omega) were determined for various values of the filter length (L) and SNR. When the weight vector is known exactly, the abs. val. (H(Omega)) function provides better resolution than Q(Omega), particularly at high SNR. When the ALE weights contain noise, and particularly at high input SNR, abs. val. (H(Omega)) is superior to Q(Omega) and S(Omega) for spectral resolution (as shown by a Monte Carlo analysis) whereas Q(Omega) and S(Omega) are more accurate than abs. val. (H(Omega)) for determining sinusoid frequency.