macleod

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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; %