DSP Blockset

Toeplitz

Generate a matrix with Toeplitz symmetry.

Library

Math Functions / Matrices and Linear Algebra / Matrix Operations

Description

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(i-1,j-1)

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

If both of the inputs are sample-based, the output is sample-based. Otherwise, the output is frame-based.

When the Symmetric check box is selected, 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

The output has the same frame status as the input.

Dialog Box

Symmetric

When selected, enables the single-input configuration for symmetric Toeplitz matrix output.

See Also

Constant Diagonal Matrix	DSP Blockset
toeplitz	MATLAB

Time-Varying Lattice Filter

To Wave Device