toeplitz

Create Toeplitz matrix

Description

example

t = toeplitz(a,b) returns a nonsymmetric Toeplitz matrix with a as its first column and b as its first row. b is cast to the numerictype of a. If one of the arguments of toeplitz is a built-in data type, it is cast to the data type of the fi object. If the first elements of a and b differ, toeplitz issues a warning and uses the column element for the diagonal.

example

t = toeplitz(b) returns the symmetric or Hermitian Toeplitz matrix formed from vector b, where b is the first row of the matrix.

Examples

collapse all

r = fi([1 2 3]);
toeplitz(r)
1     2     3

DataTypeMode: Fixed-point: binary point scaling
Signedness: Signed
WordLength: 16
FractionLength: 13

RoundingMethod: Nearest
OverflowAction: Saturate
ProductMode: FullPrecision
SumMode: FullPrecision

Tag:

ans =

1     2     3
2     1     2
3     2     1
numerictype(1,16,13)

Create a nonsymmetric Toeplitz matrix with a specified column and row vector.

toeplitz(a,b) casts b into the data type of a. In this example, overflow occurs:

fipref('NumericTypeDisplay','short');
format short g
a = fi([1 2 3],true,8,5)
b = fi([1 4 8],true,16,10)
toeplitz(a,b)
a =

1     2     3
numerictype(1,8,5)

b =

1     4     8
numerictype(1,16,10)

ans =

1       3.9688       3.9688
2            1       3.9688
3            2            1
numerictype(1,8,5)

toeplitz(b,a) casts a into the data type of b. In this example, overflow does not occur:

toeplitz(b,a)
ans =

1     2     3
4     1     2
8     4     1
numerictype(1,16,10)

If one of the arguments of toeplitz is a built-in data type, it is cast to the data type of the fi object.

x = double([1 exp(1) pi]);
toeplitz(a,x)
ans =

1       2.7188       3.1563
2            1       2.7188
3            2            1
numerictype(1,8,5)

Input Arguments

collapse all

Column of Toeplitz matrix, specified as a scalar or vector. If the first elements of a and b differ, toeplitz uses the column element for the diagonal.

Data Types: fi
Complex Number Support: Yes

Row of Toeplitz matrix, specified as a scalar or vector. If the first elements of a and b differ, toeplitz uses the column element for the diagonal.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | fi
Complex Number Support: Yes

Output Arguments

collapse all

Toeplitz matrix, returned as a fi object.

The output fi object, t, has the same numerictype properties as the leftmost fi object input. If the leftmost fi object input has a local fimath, the output fi object is assigned the same local fimath. Otherwise, the output fi object, t, has no local fimath.

Functions

Introduced before R2006a

Fixed-Point Designer Documentation Get trial now