How can we implement a butterworth filter using Python's scipy libraries?

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To implement a Butterworth filter using Python's scipy libraries, you can use the butter function from the signal module to design the filter and then filter the input signal using the lfilter function. Here are the steps:

1. Import the required libraries:

from scipy.signal import butter, lfilter

1. Define the filter parameters:

fs = 1000        # Sampling frequency
cutoff = 100     # Cutoff frequency
order = 4        # Filter order

1. Use the butter function to design the filter coefficients:

nyq = 0.5 * fs   # Nyquist frequency
normal_cutoff = cutoff / nyq   # Normalize the cutoff frequency
b, a = butter(order, normal_cutoff, btype='low', analog=False)

Here, we are specifying a low-pass filter with a cutoff frequency of 100 Hz.

1. Filter the input signal using the lfilter function:

filtered_signal = lfilter(b, a, input_signal)

This will apply the Butterworth filter to the input signal and produce the filtered signal as the output. You can then use this filtered signal for further processing or analysis.