# jax.numpy.sincÂ¶

jax.numpy.sinc(x)[source]Â¶

Return the sinc function.

LAX-backend implementation of sinc(). Original docstring below.

The sinc function is $$\sin(\pi x)/(\pi x)$$.

xndarray

Array (possibly multi-dimensional) of values for which to to calculate sinc(x).

outndarray

sinc(x), which has the same shape as the input.

sinc(0) is the limit value 1.

The name sinc is short for â€śsine cardinalâ€ť or â€śsinus cardinalisâ€ť.

The sinc function is used in various signal processing applications, including in anti-aliasing, in the construction of a Lanczos resampling filter, and in interpolation.

For bandlimited interpolation of discrete-time signals, the ideal interpolation kernel is proportional to the sinc function.

1

Weisstein, Eric W. â€śSinc Function.â€ť From MathWorldâ€“A Wolfram Web Resource. http://mathworld.wolfram.com/SincFunction.html

2

Wikipedia, â€śSinc functionâ€ť, https://en.wikipedia.org/wiki/Sinc_function

>>> import matplotlib.pyplot as plt
>>> x = np.linspace(-4, 4, 41)
>>> np.sinc(x)
array([-3.89804309e-17,  -4.92362781e-02,  -8.40918587e-02, # may vary
-8.90384387e-02,  -5.84680802e-02,   3.89804309e-17,
6.68206631e-02,   1.16434881e-01,   1.26137788e-01,
8.50444803e-02,  -3.89804309e-17,  -1.03943254e-01,
-1.89206682e-01,  -2.16236208e-01,  -1.55914881e-01,
3.89804309e-17,   2.33872321e-01,   5.04551152e-01,
7.56826729e-01,   9.35489284e-01,   1.00000000e+00,
9.35489284e-01,   7.56826729e-01,   5.04551152e-01,
2.33872321e-01,   3.89804309e-17,  -1.55914881e-01,
-2.16236208e-01,  -1.89206682e-01,  -1.03943254e-01,
-3.89804309e-17,   8.50444803e-02,   1.26137788e-01,
1.16434881e-01,   6.68206631e-02,   3.89804309e-17,
-5.84680802e-02,  -8.90384387e-02,  -8.40918587e-02,
-4.92362781e-02,  -3.89804309e-17])

>>> plt.plot(x, np.sinc(x))
[<matplotlib.lines.Line2D object at 0x...>]
>>> plt.title("Sinc Function")
Text(0.5, 1.0, 'Sinc Function')
>>> plt.ylabel("Amplitude")
Text(0, 0.5, 'Amplitude')
>>> plt.xlabel("X")
Text(0.5, 0, 'X')
>>> plt.show()