一些评论:

• 奈奎斯特频率是采样率的一半.
• 您正在使用定期采样的数据，因此需要数字滤波器而不是模拟滤波器.这意味着您不应在对butter的调用中使用analog=True，而应使用scipy.signal.freqz(而不是freqs)来生成频率响应.
• 这些简短实用程序功能的一个目标是让您保留所有以Hz表示的频率.您不必转换为弧度/秒.只要您以一致的单位表示频率，实用程序功能中的缩放就可以为您进行归一化.

• The Nyquist frequency is half the sampling rate.
• You are working with regularly sampled data, so you want a digital filter, not an analog filter. This means you should not use analog=True in the call to butter, and you should use scipy.signal.freqz (not freqs) to generate the frequency response.
• One goal of those short utility functions is to allow you to leave all your frequencies expressed in Hz. You shouldn't have to convert to rad/sec. As long as you express your frequencies with consistent units, the scaling in the utility functions takes care of the normalization for you.

这是脚本的我的修改版本，后面是脚本生成的图.

Here's my modified version of your script, followed by the plot that it generates.

import numpy as np
from scipy.signal import butter, lfilter, freqz
import matplotlib.pyplot as plt


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


# Filter requirements.
order = 6
fs = 30.0       # sample rate, Hz
cutoff = 3.667  # desired cutoff frequency of the filter, Hz

# Get the filter coefficients so we can check its frequency response.
b, a = butter_lowpass(cutoff, fs, order)

# Plot the frequency response.
w, h = freqz(b, a, worN=8000)
plt.subplot(2, 1, 1)
plt.plot(0.5*fs*w/np.pi, np.abs(h), 'b')
plt.plot(cutoff, 0.5*np.sqrt(2), 'ko')
plt.axvline(cutoff, color='k')
plt.xlim(0, 0.5*fs)
plt.title("Lowpass Filter Frequency Response")
plt.xlabel('Frequency [Hz]')
plt.grid()


# Demonstrate the use of the filter.
# First make some data to be filtered.
T = 5.0         # seconds
n = int(T * fs) # total number of samples
t = np.linspace(0, T, n, endpoint=False)
# "Noisy" data.  We want to recover the 1.2 Hz signal from this.
data = np.sin(1.2*2*np.pi*t) + 1.5*np.cos(9*2*np.pi*t) + 0.5*np.sin(12.0*2*np.pi*t)

# Filter the data, and plot both the original and filtered signals.
y = butter_lowpass_filter(data, cutoff, fs, order)

plt.subplot(2, 1, 2)
plt.plot(t, data, 'b-', label='data')
plt.plot(t, y, 'g-', linewidth=2, label='filtered data')
plt.xlabel('Time [sec]')
plt.grid()
plt.legend()

plt.subplots_adjust(hspace=0.35)
plt.show()