esprit_ls.m

统计自适应信号处理的matlab程序

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%
% FUNCTION: esprit_ls.m
%
% AUTHOR: Steve Kogon
% 
% DATE: January 20, 1999
%
% DESCRIPTION: This file estimates the frequencies of sinusoids using 
%              least squares ESPRIT algorithm (Roy & Kailath 1989).
%
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%
%-----------------------------------------------------------
% Copyright 2000, by Dimitris G. Manolakis, Vinay K. Ingle,
% and Stephen M. Kogon.  For use with the book
% "Statistical and Adaptive Signal Processing"
% McGraw-Hill Higher Education.
%-----------------------------------------------------------


function [fest] = esprit_ls(x,P,M)
% x = signal
% P = number of complex exponentials
% M = time-window length
% Nfft = number of FFT frequencies
N = length(x) - M + 1;

% Form data matrix from the signal x(n)
X = zeros(N,M);
for n = 1:M
   X(:,n) = x((1:N) + (M-n));
end

% Compute the SVD of the augmented data matrix
[L,S,U] = svd(X);

% Signal subspace (2*N by K matrix of right singular vectors)
Us = U(:,1:P);

% Split subspace into two subspaces corresponding to the unshifted
% and shifted versions
U1 = Us(1:(M-1),:);
U2 = Us(2:M,:);

% Solve for the rotation between these subspaces (LS version)
Psi = U1\U2;

% Solve for the original rotation that was needed for the original data
phi = eig(Psi);

% Estimate frequencies
fest = angle(phi)/(2*pi);