numpy.sinc(x)
[source]
Return the sinc function.
The sinc function is .
Parameters: |
x : ndarray Array (possibly multi-dimensional) of values for which to to calculate |
---|---|
Returns: |
out : ndarray
|
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.
[R282] | Weisstein, Eric W. “Sinc Function.” From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/SincFunction.html |
[R283] | Wikipedia, “Sinc function”, http://en.wikipedia.org/wiki/Sinc_function |
>>> x = np.linspace(-4, 4, 41) >>> np.sinc(x) array([ -3.89804309e-17, -4.92362781e-02, -8.40918587e-02, -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") <matplotlib.text.Text object at 0x...> >>> plt.ylabel("Amplitude") <matplotlib.text.Text object at 0x...> >>> plt.xlabel("X") <matplotlib.text.Text object at 0x...> >>> plt.show()
It works in 2-D as well:
>>> x = np.linspace(-4, 4, 401) >>> xx = np.outer(x, x) >>> plt.imshow(np.sinc(xx)) <matplotlib.image.AxesImage object at 0x...>
© 2008–2017 NumPy Developers
Licensed under the NumPy License.
https://docs.scipy.org/doc/numpy-1.12.0/reference/generated/numpy.sinc.html