Toeplitz
Generate matrix with Toeplitz symmetry
Libraries:
DSP System Toolbox /
Math Functions /
Matrices and Linear Algebra /
Matrix Operations
Description
Generate a symmetric or asymmetric Toeplitz matrix from inputs. If you select the Symmetric check box, the block generates a symmetric (or Hermitian) Toeplitz matrix. If you do not select the Symmetric check box, the block generates an asymmetric Toeplitz matrix. The columns and rows are specified by the first and second inputs, respectively. The first matrix element is inherited from the column.
Ports
Input
Input — Input
vector
Input u
from which the block generates a symmetric
(or Hermitian) Toeplitz matrix when you select the
Symmetric check box. The single input defines
both the first row and first column of the Toeplitz matrix.
Here is the equivalent MATLAB® code.
y = toeplitz(u)
The output y has the dimension
[length
(u
)
length
(u
)]. For example, the
Toeplitz matrix generated from the input vector [1 2 3
4]
is
Dependencies
To enable this port, select the Symmetric check box.
Data Types: single
| double
| int8
| int16
| int32
| uint8
| uint16
| uint32
| Boolean
| fixed point
Complex Number Support: Yes
Toep Col — First column of asymmetric Toeplitz matrix
vector
First column of the asymmetric Toeplitz matrix, specified as a vector.
Dependencies
To enable this port, clear the Symmetric check box.
Data Types: single
| double
| int8
| int16
| int32
| uint8
| uint16
| uint32
| Boolean
| fixed point
Complex Number Support: Yes
Toep Row — First row of asymmetric Toeplitz matrix
vector
First row of the asymmetric Toeplitz matrix, specified as a vector.
Dependencies
To enable this port, clear the Symmetric check box.
Data Types: single
| double
| int8
| int16
| int32
| uint8
| uint16
| uint32
| Boolean
| fixed point
Complex Number Support: Yes
Output
Output — Toeplitz matrix
matrix
Toeplitz matrix, returned as a matrix. The block generates this matrix depending on the setting of the Symmetric check box.
When you select the Symmetric check box, the
block generates a symmetric (or Hermitian) Toeplitz matrix from a single
input u
defining both the first row and first column
of the matrix.
Here is the equivalent MATLAB code.
y = toeplitz(u)
The output has dimension
[length
(u
)
length
(u
)]. For example, the
Toeplitz matrix generated from the input vector [1 2 3
4]
is
When you do not select the Symmetric check box,
the Toeplitz block generates a Toeplitz matrix from
inputs defining the first column and first row. The top input
(Toep Col
) is a vector containing the values to
be placed in the first column of the matrix, and the bottom input
(Toep Row
) is a vector containing the values to
be placed in the first row of the matrix.
Here is the equivalent MATLAB code.
y = toeplitz(Toep Col,Toep Row)
The other elements of the matrix obey the relationship:
y(i,j) = y(i-1,j-1)
and the output has dimension
[length
(Toep Col
)
length
(Toep Row
)]. The
y(1,1) element is inherited from the
Toep Col
input. For example, the following
inputs
Toep Col = [1 2 3 4 5]
Toep Row = [7 7 3 3 2 1 3]
produce the Toeplitz matrix
Data Types: single
| double
| int8
| int16
| int32
| uint8
| uint16
| uint32
| Boolean
| fixed point
Complex Number Support: Yes
Parameters
Symmetric — Symmetric Toeplitz matrix output
on
(default) | off
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.
Here is the equivalent MATLAB code.
y = toeplitz(u)
When you do not select the Symmetric check box, the
Toeplitz block generates a Toeplitz matrix from inputs
defining the first column Toep Col
and first row
Toep Row
.
Here is the equivalent MATLAB code.
y = toeplitz(Toep Col,Toep Row)
The other elements of the matrix obey the relationship:
y(i,j) = y(i-1,j-1)
For more information, see the Output port description.
Saturate on integer overflow — Saturate on integer overflow
on
(default) | off
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 ignored for floating-point signals.
Dependencies
To enable this parameter, select the Symmetric check box.
Block Characteristics
Data Types |
|
Direct Feedthrough |
|
Multidimensional Signals |
|
Variable-Size Signals |
|
Zero-Crossing Detection |
|
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.
Version History
Introduced before R2006a
See Also
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