python-scipyHow do I use a Python Scipy Butterworth filter?

To use a Python Scipy Butterworth filter, the following steps should be taken:

1. Import the necessary modules:

import scipy.signal as signal
import numpy as np

2. Create a signal. For example, a sine wave:

fs = 10e3
N = 1e5
amp = 2*np.sqrt(2)
freq = 1234.0
noise_power = 0.001 * fs / 2
time = np.arange(N) / float(fs)
x = amp*np.sin(2*np.pi*freq*time)
x += np.random.normal(scale=np.sqrt(noise_power), size=time.shape)

3. Create a Butterworth filter of order 3, with a cutoff frequency of 700 Hz:

b, a = signal.butter(3, 700/(fs/2), btype='low')

4. Apply the filter to the signal:

filtered_x = signal.lfilter(b, a, x)

5. Plot the original and filtered signals:

import matplotlib.pyplot as plt
plt.plot(time, x, label='Noisy signal')
plt.plot(time, filtered_x, label='Filtered signal (%g Hz)' % f0)
plt.xlabel('time (seconds)')
plt.hlines([-amp, amp], 0, time[-1], linestyles='--')
plt.grid(True)
plt.axis('tight')
plt.legend(loc='upper left')
plt.show()

Code explanation

**

1. import scipy.signal as signal: This imports the signal module from the scipy package, which contains functions for signal processing.
2. import numpy as np: This imports the numpy package, which provides useful functions for array manipulation.
3. fs = 10e3: This sets the sampling frequency of the signal to 10 kHz.
4. N = 1e5: This sets the number of samples in the signal to 100,000.
5. amp = 2*np.sqrt(2): This sets the amplitude of the signal to 2√2.
6. freq = 1234.0: This sets the frequency of the signal to 1234 Hz.
7. noise_power = 0.001 * fs / 2: This sets the power of the noise to 0.001 times the sampling frequency divided by 2.
8. time = np.arange(N) / float(fs): This creates an array of N samples, evenly spaced in time, with the sampling frequency set to fs.
9. x = amp*np.sin(2*np.pi*freq*time): This creates a sine wave with the given amplitude, frequency, and sampling frequency.
10. x += np.random.normal(scale=np.sqrt(noise_power), size=time.shape): This adds random noise to the signal with the given noise power.
11. b, a = signal.butter(3, 700/(fs/2), btype='low'): This creates a Butterworth filter of order 3 and cutoff frequency of 700 Hz.
12. filtered_x = signal.lfilter(b, a, x): This applies the filter to the signal.
13. import matplotlib.pyplot as plt: This imports the matplotlib package, which provides functions for plotting.
14. plt.plot(time, x, label='Noisy signal'): This plots the noisy signal.
15. plt.plot(time, filtered_x, label='Filtered signal (%g Hz)' % f0): This plots the filtered signal.
16. plt.xlabel('time (seconds)'): This sets the x-axis label to "time (seconds)".
17. plt.hlines([-amp, amp], 0, time[-1], linestyles='--'): This plots horizontal lines at the given amplitudes.
18. plt.grid(True): This turns on the grid.
19. plt.axis('tight'): This sets the axis limits to the range of the data.
20. plt.legend(loc='upper left'): This adds a legend to the plot.
21. plt.show(): This displays the plot.

Relevant Links

• Scipy Signal Processing
• Numpy Reference
• Matplotlib Tutorial

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