numpy.sinc#

numpy.sinc(x)[source]#

Return the normalized sinc function.

The sinc function is equal to \(\sin(\pi x)/(\pi x)\) for any argument \(x\ne 0\). sinc(0) takes the limit value 1, making sinc not only everywhere continuous but also infinitely differentiable.

Note

Note the normalization factor of pi used in the definition. This is the most commonly used definition in signal processing. Use sinc(x / np.pi) to obtain the unnormalized sinc function \(\sin(x)/x\) that is more common in mathematics.

Parameters:

xndarray

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

Returns:

outndarray

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

Notes

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.

Array API Standard Support

sinc has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

Library	CPU	GPU
NumPy		n/a
CuPy	n/a
PyTorch
JAX
Dask		n/a

See Support for the array API standard for more information.

References

[1]

Weisstein, Eric W. Sinc Function. From MathWorldA Wolfram Web Resource. https://mathworld.wolfram.com/SincFunction.html

[2]

Wikipedia, Sinc function, https://en.wikipedia.org/wiki/Sinc_function

Examples

Try it in your browser!

>>> import numpy as np
>>> 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()

[../../_images/numpy-sinc-1.png]

Go BackOpen In Tab