Generate matrix with Toeplitz symmetry
Math Functions / Matrices and Linear Algebra / Matrix Operations
dspmtrx3
The Toeplitz block generates a Toeplitz matrix from inputs defining
the first column and first row. The top input (Col
)
is a vector containing the values to be placed in the first column of
the matrix, and the bottom input (Row
) is a vector
containing the values to be placed in the first row of
the matrix.
y = toeplitz(Col,Row) % Equivalent MATLAB code
The other elements of the matrix obey the relationship
y(i,j) = y(i1,j1)
and the output has dimension [length(Col) length(Row)]
.
The y(1,1) element is inherited from the Col
input.
For example, the following inputs
Col = [1 2 3 4 5] Row = [7 7 3 3 2 1 3]
produce the Toeplitz matrix
$$\left[\begin{array}{ccccccc}1& 7& 3& 3& 2& 1& 3\\ 2& 1& 7& 3& 3& 2& 1\\ 3& 2& 1& 7& 3& 3& 2\\ 4& 3& 2& 1& 7& 3& 3\\ 5& 4& 3& 2& 1& 7& 3\end{array}\right]$$
When you select the Symmetric check box,
the block generates a symmetric (Hermitian) Toeplitz matrix from a
single input, u
, defining both the first row and
first column of the matrix.
y = toeplitz(u) % Equivalent MATLAB code
The output has dimension [length(u) length(u)]
.
For example, the Toeplitz matrix generated from the input vector [1
2 3 4]
is
$$\left[\begin{array}{cccc}1& 2& 3& 4\\ 2& 1& 2& 3\\ 3& 2& 1& 2\\ 4& 3& 2& 1\end{array}\right]$$
The Toeplitz block supports real and complex floatingpoint and fixedpoint inputs.
When selected, enables the singleinput configuration for symmetric Toeplitz matrix output.
When you generate a symmetric Toeplitz matrix with this block, if the input vector is complex, the output is a symmetric Hermitian matrix whose elements satisfy the relationship
$$y(i,j)=\mathrm{conj}(y(j,i))$$
For fixedpoint signals the conjugate operation could result in an overflow. When you select this parameter, overflows saturate. This parameter is only visible with the Symmetric parameter is selected. This parameter is ignored for floatingpoint signals.
Port  Supported Data Types 

Input 

Toep Col 

Toep Row 

Output 

toeplitz  MATLAB 