傅立叶级数适合Python

sympy如果愿意，可以使用我为此目的编写的程序包，与数据拟合代码保持非常接近的状态symfit。它基本上是scipy使用sympy接口包装的。使用symfit，您可以执行以下操作：

from symfit import parameters, variables, sin, cos, Fit
import numpy as np
import matplotlib.pyplot as plt

def fourier_series(x, f, n=0):
    """
    Returns a symbolic fourier series of order `n`.

    :param n: Order of the fourier series.
    :param x: Independent variable
    :param f: Frequency of the fourier series
    """
    # Make the parameter objects for all the terms
    a0, *cos_a = parameters(','.join(['a{}'.format(i) for i in range(0, n + 1)]))
    sin_b = parameters(','.join(['b{}'.format(i) for i in range(1, n + 1)]))
    # Construct the series
    series = a0 + sum(ai * cos(i * f * x) + bi * sin(i * f * x)
                     for i, (ai, bi) in enumerate(zip(cos_a, sin_b), start=1))
    return series

x, y = variables('x, y')
w, = parameters('w')
model_dict = {y: fourier_series(x, f=w, n=3)}
print(model_dict)

这将打印出我们想要的符号模型：

{y: a0 + a1*cos(w*x) + a2*cos(2*w*x) + a3*cos(3*w*x) + b1*sin(w*x) + b2*sin(2*w*x) + b3*sin(3*w*x)}

接下来，我将其设置为简单的步进函数，以向您展示其工作原理：

# Make step function data
xdata = np.linspace(-np.pi, np.pi)
ydata = np.zeros_like(xdata)
ydata[xdata > 0] = 1
# Define a Fit object for this model and data
fit = Fit(model_dict, x=xdata, y=ydata)
fit_result = fit.execute()
print(fit_result)

# Plot the result
plt.plot(xdata, ydata)
plt.plot(xdata, fit.model(x=xdata, **fit_result.params).y, color='green', ls=':')

这将打印：

Parameter Value        Standard Deviation
a0        5.000000e-01 2.075395e-02
a1        -4.903805e-12 3.277426e-02
a2        5.325068e-12 3.197889e-02
a3        -4.857033e-12 3.080979e-02
b1        6.267589e-01 2.546980e-02
b2        1.986491e-02 2.637273e-02
b3        1.846406e-01 2.725019e-02
w         8.671471e-01 3.132108e-02
Fitting status message: Optimization terminated successfully.
Number of iterations:   44
Regression Coefficient: 0.9401712713086535

并产生以下图：

就这么简单！我把剩下的留给你想象。有关更多信息，请参见此处的文档。