使用lmfit将信号拟合为方波

import numpy as np
from lmfit import Model

# 定义方波模型函数
def square_wave(x, amplitude, frequency, duty_cycle, offset):
    period = 1 / frequency
    t = (x - offset) % period / period
    return np.where(t < duty_cycle, amplitude, -amplitude)

# 创建模型对象
model = Model(square_wave)

# 生成模拟数据
x = np.linspace(0, 10, 1000)
amplitude_true = 1.0
frequency_true = 2.0
duty_cycle_true = 0.5
offset_true = 0.0
y_true = square_wave(x, amplitude_true, frequency_true, duty_cycle_true, offset_true)
y_noise = np.random.normal(0, 0.1, x.shape)
y = y_true + y_noise

# 设置初始参数估计
params = model.make_params(amplitude=0.5, frequency=1.5, duty_cycle=0.3, offset=0.0)

# 执行拟合
result = model.fit(y, params, x=x)

# 输出拟合结果
print(result.fit_report())

# 绘制拟合曲线和原始数据
import matplotlib.pyplot as plt
plt.plot(x, y, 'b.', label='Noisy data')
plt.plot(x, y_true, 'g--', label='True data')
plt.plot(x, result.best_fit, 'r-', label='Best fit')
plt.legend()
plt.show()