corrmtx Generate data matrix for autocorrelation matrix estimation X = corrmtx(x,m) [X,R] = corrmtx(x,m) X = corrmtx(x,m,s) [X,R] = corrmtx(x,m,s) x: input vector of size N for which correlation matrix of size m is to be calculated m: size of correlation matrix to be computed. Positive integer strictly smaller than the length of the input x X: data matrix as specified according to the input 'method' s: method for type of output matrix X 'autocorrelation': (default) X is the (n + m)-by-(m + 1) rectangular Toeplitz matrix that generates an autocorrelation estimate for the leng th-n data vector x, derived using prewindowed and postwindowed data, based on an mth-order prediction error model. 'prewindowed': X is the n-by-(m + 1) rectangular Toeplitz matrix that generates an autocorrelation estimate for the length-n data vector x, derived using prewindowed data, based on an mth-order prediction error model. 'postwindowed': X is the n-by-(m + 1) rectangular Toeplitz matrix that generates an autocorrelation estimate for the length-n data vector x , derived using postwindowed data, based on an mth-order prediction error model. 'covariance': X is the (n – m)-by-(m + 1) rectangular Toeplitz matrix that generates an autocorrelation estimate for the length-n data vect or x, derived using nonwindowed data, based on an mth-order prediction error model. 'modified': X is the 2(n – m)-by-(m + 1) modified rectangular Toeplitz matrix that generates an autocorrelation estimate for the length-n d ata vector x, derived using forward and backward prediction error estimates, based on an mth-order prediction error model. R: (m + 1)-by-(m + 1) autocorrelation matrix estimate calculated as X'*X Consider the generic matrix X below _ _ | x(1) ..........0 | | : . : | | : . : | | x(m+1).......x(1)| | : . : | | : . : | X = | x(n-m).....x(m+1)| | : . : | | : . : | | x(n).......x(n-m)| | : . : | | : . : | |_0 ..........x(n)_| -- For different inputs of string s the output would vary ass described below 'autocorrelation' — (default) X = X, above. 'prewindowed' — X is the n-by-(m + 1) submatrix of X whose first row is [x(1) … 0] and whose last row is [x(n) … x(n – m)] 'postwindowed' — X is the n-by-(m + 1) submatrix of X whose first row is [x(m + 1) … x(1)] and whose last row is [0 … x(n)] 'covariance' — X is the (n – m)-by-(m + 1) submatrix of X whose first row is [x(m + 1) … x(1)] and whose last row is [x(n) … x(n – m)] 'modified' — X is the 2(n – m)-by-(m + 1) matrix X_mod shown below _ _ | x(m+1) ......x(1)| | : . : | | : . : | | x(n-m).....x(m+1)| | : . : | | : . : | | x(n).......x(n-m)| X_mod= | x*(1).....x*(m+1)| | : . : | | : . : | | x*(m+1)...x*(n-m)| | : . : | | : . : | |_x*(n-m) ...x*(n)_| peig pmusic rooteig rootmusic xcorr Author: Pandit Bilbligraphy S. Lawrence. Digital Spectral Analysis. Englewood Cliffs, NJ: Prentice-Hall, 1987.