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# scipy.special.sinc

`scipy.special.``sinc`(x)

  Return the sinc function.

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

  Parameters: | x : ndarray Array (possibly multi-dimensional) of values for which to to calculate `sinc(x)`.
  Returns: | out : ndarray `sinc(x)`, which has the same shape as the input.

  Notes

  `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.

  References

  [R518] | Weisstein, Eric W. “Sinc Function.” From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/SincFunction.html

  [R519] | Wikipedia, “Sinc function”, http://en.wikipedia.org/wiki/Sinc_function

  Examples

      >>> 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...>