Signal Processing Blockset™

Toeplitz - Generate matrix with Toeplitz symmetry

Library

Math Functions / Matrices and Linear Algebra / Matrix Operations

dspmtrx3

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

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

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

The output has the same frame status as the input.

The Toeplitz block supports real and complex floating-point and fixed-point inputs.

Dialog Box

Symmetric

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

Saturate on integer overflow

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

For fixed-point 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 floating-point signals.

Supported Data Types

See Also

Time-Varying Lattice Filter

To Audio Device