% function [x] = macleod(Y)
% Adapted by Eric Jacobsen, June 2002.
%
% Y is a three-element complex vector with the
% DFT output magnitude maximizer as the center element.
%
% Returns -0.5 < x < 0.5, which is the fraction of the sample
% spacing (i.e., bin width) about the center element where the
% peak is estimated to be.
%
% Ref: Macleod, M.D., "Fast Nearly ML Estimation of the Parameters
% of Real or Complex Single Tones or Resolved Multiple Tones,"
% IEEE Trans. Sig. Proc. Vol 46 No 1,
% January 1998, pp141-148.
ref = Y(2); % Isolate phase reference.
R = real(Y.*conj(ref)); % Generate phase corrected coefficient vector.
gamma = (R(1)-R(3))/((2*R(2))+R(1)+R(3)); % Calculate offset.
delta = (sqrt(1 + 8*gamma*gamma)-1)/(4*gamma); % Final estimate.
x = delta;
%