Contents Previous Next Subchapters

Constructing Toeplitz Matrices
Syntax t = toeplitz(c)
t = toeplitz(cr)
See Also levinson

Description
Constructs a Toeplitz matrix with first its first column equal to the vector c and its first row equal to the vector r. If the argument r is not present, its default value is the complex conjugate of c. If the first element of r is not equal to the first element of c, the first element of c is used for the diagonal of the matrix.

If the vectors c and r have equal length n, the return matrix is
         / c   r    r   ...  r    \
         |  1   2    3        n   |
         |                        |
         | c   c    r   ...  r    |
         |  2   1    2        n-1 |
     t = | .    .   .        .    |
         | .    .     .      .    |
         | .    .       .    .    |
         |                        |
         | c   c    c   ...  c    |
         \  n   n-1  n-2      1   /


In general, if n is the length of c and m is the length of r, the return value t is an n x m matrix with
              / c           if i - j > 0
             /   i - j + 1
     t    = < 
      i,j    \  r           if j - i > 0
              \  j - i + 1 
The type of t is the type that results from coercion between the type of c and r.

Example
If you enter
     c = [ 1 , 2 , 3 ]
     toeplitz(c)
O-Matrix will reply
     {
     [ 1 , 2 , 3 ]
     [ 2 , 1 , 2 ]
     [ 3 , 2 , 1 ]
     }