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numpy.sinc

numpy.sinc(x)[source]

返回sinc函数。

sinc函数为\sin(\pi x)/(\pi x)

参数:

x:ndarray

要计算sinc(x)的值的数组(可能是多维的)。

返回:

out:ndarray

sinc(x),其具有与输入相同的形状。

笔记

sinc(0)是极限值1。

名称sinc是“sine cardinal”或“sinus cardinalis”的缩写。

sinc函数用于各种信号处理应用中,包括抗锯齿,Lanczos重采样滤波器的构造和插值。

对于离散时间信号的带限内插,理想内插核与sinc函数成比例。

参考文献

[R282]Weisstein,Eric W.“Sinc Function。”来自MathWorld-Wolfram Web资源。http://mathworld.wolfram.com/SincFunction.html
[R283]维基百科,“Sinc函数”,http://en.wikipedia.org/wiki/Sinc_function

例子

>>> 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()

它也工作在2-D:

>>> x = np.linspace(-4, 4, 401)
>>> xx = np.outer(x, x)
>>> plt.imshow(np.sinc(xx))
<matplotlib.image.AxesImage object at 0x...>