mars.tensor.sinc

mars.tensor.sinc(x, **kwargs)[source]

Return the sinc function.

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

x : Tensor
Tensor (possibly multi-dimensional) of values for which to to calculate sinc(x).
out : Tensor
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.

[1]Weisstein, Eric W. “Sinc Function.” From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/SincFunction.html
[2]Wikipedia, “Sinc function”, http://en.wikipedia.org/wiki/Sinc_function
>>> import mars.tensor as mt
>>> x = mt.linspace(-4, 4, 41)
>>> mt.sinc(x).execute()
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])
>>> import matplotlib.pyplot as plt
>>> plt.plot(x.execute(), np.sinc(x).execute())
[<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()