Return the sinc function.

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

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


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


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

sinc(0) is the limit value 1.

The name sinc is short for “sine cardinal” or “sinus cardinalis”.

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.


Weisstein, Eric W. “Sinc Function.” From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/SincFunction.html


Wikipedia, “Sinc function”, 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()