aliasing

import numpy as np
from scipy.signal import butter, lfilter

def butter_lowpass(cutoff, fs, order=5):
    nyq = 0.5 * fs
    normal_cutoff = cutoff / nyq
    b, a = butter(order, normal_cutoff, btype='low', analog=False)
    return b, a

def butter_lowpass_filter(data, cutoff, fs, order=5):
    b, a = butter_lowpass(cutoff, fs, order=order)
    y = lfilter(b, a, data)
    return y

# 示例音频信号
fs = 1000  # 采样率
t = np.arange(0, 1, 1/fs)
f1 = 50  # 低频信号
f2 = 500  # 高频信号
signal = np.sin(2 * np.pi * f1 * t) + 0.5 * np.sin(2 * np.pi * f2 * t)

# 混叠效应
signal_downsampled = signal[::10]  # 采样率降低10倍

# 抗混叠滤波
cutoff = 200  # 截止频率
filtered_signal = butter_lowpass_filter(signal_downsampled, cutoff, fs)

# 比较原始信号和滤波后的信号
import matplotlib.pyplot as plt

plt.figure(figsize=(12, 6))
plt.subplot(2, 1, 1)
plt.plot(t, signal, label='Original Signal')
plt.plot(t[::10], signal_downsampled, 'r.', label='Downsampled Signal')
plt.legend()
plt.subplot(2, 1, 2)
plt.plot(t[::10], filtered_signal, 'g', label='Filtered Signal')
plt.legend()
plt.show()