numpy.sinc

numpy.sinc(x)

返回归一化的sinc函数.

sinc 函数对于任何参数 \(x\ne 0\) 等于 \(\sin(\pi x)/(\pi x)\).``sinc(0)`` 取极限值 1,使得 sinc 不仅在各处连续,而且无限可微.

备注

注意在定义中使用的 pi 的归一化因子.这是信号处理中最常用的定义.使用 sinc(x / np.pi) 来获得在数学中更常见的未归一化的 sinc 函数 \(\sin(x)/x\).

参数:

xndarray

要计算 sinc(x) 的值的数组（可能是多维的）.

返回:

outndarray

sinc(x),其形状与输入相同.

备注

sinc 这个名字是 “sine cardinal” 或 “sinus cardinalis” 的缩写.

sinc 函数在各种信号处理应用中使用,包括在抗混叠、在构建 Lanczos 重采样滤波器和在插值中.

对于离散时间信号的带限插值,理想的插值核与sinc函数成正比.

参考文献

[1]

Weisstein, Eric W. “Sinc 函数.” 来自 MathWorld–A Wolfram 网络资源.https://mathworld.wolfram.com/SincFunction.html

[2]

Wikipedia, “Sinc 函数”, https://en.wikipedia.org/wiki/Sinc_function

示例

>>> 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()