如何计算Numpy中的傅立叶级数? [英] How to calculate a Fourier series in Numpy?

问题描述

我有一个周期T的周期函数，想知道如何获得傅立叶系数的列表.我尝试使用numpy中的 fft 模块，但是似乎比级数更专注于傅立叶变换. 也许缺乏数学知识，但我看不到如何从fft计算傅立叶系数.

I have a periodic function of period T and would like to know how to obtain the list of the Fourier coefficients. I tried using fft module from numpy but it seems more dedicated to Fourier transforms than series. Maybe it a lack of mathematical knowledge, but I can't see how to calculate the Fourier coefficients from fft.

感谢帮助和/或示例.

推荐答案

最后，最简单的方法(使用riemann和计算系数)是解决我的问题的最可移植/最有效/最可靠的方法:

In the end, the most simple thing (calculating the coefficient with a riemann sum) was the most portable/efficient/robust way to solve my problem:

def cn(n):
   c = y*np.exp(-1j*2*n*np.pi*time/period)
   return c.sum()/c.size

def f(x, Nh):
   f = np.array([2*cn(i)*np.exp(1j*2*i*np.pi*x/period) for i in range(1,Nh+1)])
   return f.sum()

y2 = np.array([f(t,50).real for t in time])

plot(time, y)
plot(time, y2)

给我:

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