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Symbolic Math Toolbox
Mathematics
Mathematical Functions
Special Functions
Dirac and Heaviside Functions
kroneckerDelta
ON THIS PAGE
Syntax
Description
Examples
o Compare Two Symbolic Variables
o Compare Symbolic Variable with Zero
o Compare Vector of Numbers with Symbolic Variable
o Compare Two Matrices
o Use kroneckerDelta in Inputs to Other Functions
o Filter Response to Kronecker Delta Input
Input Arguments
More About
See Also
kroneckerDelta
Kronecker delta function
collapse all in page
Syntax
kroneckerDelta(m)
example
kroneckerDelta(m,n)
example
Description
example
kroneckerDelta(m) returns 1 if m == 0 and 0 if m ~= 0.
example
kroneckerDelta(m,n) returns 1 if m == n and 0 if m ~= n.
Examples
Compare Two Symbolic Variables
Set symbolic variable m equal to symbolic variable n and test their equality
using kroneckerDelta.
syms m n
m = n;
kroneckerDelta(m, n)
ans =
1
kroneckerDelta returns 1 indicating that the inputs are equal.
Compare symbolic variables p and q.
syms p q
kroneckerDelta(p, q)
ans =
kroneckerDelta(p - q, 0)
kroneckerDelta cannot decide if p == q and returns the function call with the undecidable
input. Note that kroneckerDelta(p, q) is equal to kroneckerDelta(p - q, 0).
To force a logical result for undecidable inputs, use isAlways. The isAlways function issues
a warning and returns logical 0 (false) for undecidable inputs. Set the Unknown option
to false to suppress the warning.
isAlways(kroneckerDelta(p, q), 'Unknown', 'false')
ans =
0
Compare Symbolic Variable with Zero
Set symbolic variable m to 0 and test m for equality with 0. The kroneckerDelta function errors
because it does not accept numeric inputs of type double.
m = 0;
kroneckerDelta(m)
Undefined function 'kroneckerDelta' for input arguments of type 'double'.
Use sym to convert 0 to a symbolic object before assigning it to m. This is
because kroneckerDelta only accepts symbolic inputs.
syms m
m = sym(0);
kroneckerDelta(m)
ans =
1
kroneckerDelta returns 1 indicating that m is equal to 0. Note that kroneckerDelta(m) is equal
to kroneckerDelta(m, 0).
Compare Vector of Numbers with Symbolic Variable
Compare a vector of numbers [1 2 3 4] with symbolic variable m. Set m to 3.
V = 1:4
syms m
m = sym(3)
sol = kroneckerDelta(V, m)
V =
1 2 3 4
m =
3
sol =
[ 0, 0, 1, 0]
kroneckerDelta acts on V element-wise to return a vector, sol, which is the same size as V.
The third element of sol is 1 indicating that the third element of V equals m.
Compare Two Matrices
Compare matrices A and B.
Declare matrices A and B.
syms m
A = [m m+1 m+2;m-2 m-1 m]
B = [m m+3 m+2;m-1 m-1 m+1]
A =
[ m, m + 1, m + 2]
[ m - 2, m - 1, m]
B =
[ m, m + 3, m + 2]
[ m - 1, m - 1, m + 1]
Compare A and B using kroneckerDelta.
sol = kroneckerDelta(A, B)
sol =
[ 1, 0, 1]
[ 0, 1, 0]
kroneckerDelta acts on A and B element-wise to return the matrix sol which is the same size
as A and B. The elements of sol that are 1 indicate that the corresponding elements
of A and B are equal. The elements of sol that are 0 indicate that the corresponding
elements of A and B are not equal.
Use kroneckerDelta in Inputs to Other Functions
kroneckerDelta appears in the output of iztrans.
syms z n
sol = iztrans(1/(z-1), z, n)
sol =
1 - kroneckerDelta(n, 0)
Use this output as input to ztrans to return the initial input expression.
ztrans(sol, n, z)
ans =
z/(z - 1) - 1
Filter Response to Kronecker Delta Input
Use filter to find the response of a filter when the input is the Kronecker Delta function.
Convert k to a symbolic vector using sym because kroneckerDelta only accepts symbolic
inputs, and convert it back to double using double. Provide arbitrary filter
coefficients a and b for simplicity.
b = [0 1 1];
a = [1 -0.5 0.3];
k = -20:20;
x = double(kroneckerDelta(sym(k)));
y = filter(b,a,x);
plot(k,y)
Input Arguments
collapse all
m Inputnumber | vector | matrix | multidimensional array | symbolic number | symbolic vector | symbolic matrix |
symbolic function | symbolic multidimensional array
Input, specified as a number, vector, matrix, multidimensional array, or a symbolic number,
vector, matrix, function, or multidimensional array. At least one of the inputs, m or n, must be
symbolic.
n Inputnumber | vector | matrix | multidimensional array | symbolic number | symbolic vector | symbolic matrix |
symbolic function | symbolic multidimensional array
Input, specified as a number, vector, matrix, multidimensional array, or a symbolic number,
vector, matrix, function, or multidimensional array. At least one of the inputs, m or n, must be
symbolic.
More About
expand all
Kronecker Delta Function
The Kronecker delta function is defined as
{
( )
m,n = 01if mif mn=n
Tips
When m or n is NaN, the kroneckerDelta function
returns NaN.
See Also
iztrans | ztrans
Introduced in R2014b
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