sinc
Normalized sinc function
Syntax
Description
Examples
Sinc Function of Symbolic Inputs
Create a sinc
function of a symbolic variable x
.
syms x
sinc(x)
ans =
Show that sinc
returns 1
at 0
, 0
at other integer inputs, and exact symbolic values for other inputs.
V = sym([-1 0 1 3/2]); S = sinc(V)
S =
Convert the exact symbolic output to high-precision floating point by using vpa
.
vpa(S)
ans =
Fourier Transforms Involving Sinc Function
Although sinc
can appear in tables of Fourier transforms, fourier
does not return sinc
in output.
Show that fourier
transforms a pulse in terms of sin
and cos
.
syms x
fourier(rectangularPulse(x))
ans =
Show that fourier
transforms sinc
in terms of heaviside
.
fourier(sinc(x))
ans =
Plot Sinc Function
Rewrite Sinc Function to Other Functions
Rewrite the sinc
function to the exponential function exp
by using rewrite
.
syms x rewrite(sinc(x),'exp')
ans =
Differentiate, Integrate, and Expand the Sinc Function
Differentiate, integrate, and expand sinc
by using the diff
, int
, and taylor
functions, respectively.
Differentiate sinc
.
syms x
diff(sinc(x))
ans =
Integrate sinc
from -Inf
to Inf
.
int(sinc(x),[-Inf Inf])
ans =
Integrate sinc
from -Inf
to x
.
int(sinc(x),-Inf,x)
ans =
Find the Taylor expansion of sinc
.
taylor(sinc(x))
ans =
Prove Identity Involving Sinc Function
Prove an identity by defining the identity as a condition and using the isAlways
function to check the condition.
Prove the identity .
syms x
cond = sinc(x) == 1/(gamma(1+x)*gamma(1-x));
isAlways(cond)
ans = logical
1
Input Arguments
x
— Input
number | vector | matrix | array | symbolic number | symbolic variable | symbolic array | symbolic function | symbolic expression
Input, specified as a number, vector, matrix, or array, or a symbolic number, variable, array, function, or expression.
Version History
Introduced in R2018b
See Also
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