butter#
- scipy.signal.butter(N, Wn, btype='low', analog=False, output='ba', fs=None)[source]#
- Butterworth digital and analog filter design. - Design an Nth-order digital or analog Butterworth filter and return the filter coefficients. - Parameters:
- Nint
- The order of the filter. For ‘bandpass’ and ‘bandstop’ filters, the resulting order of the final second-order sections (‘sos’) matrix is - 2*N, with N the number of biquad sections of the desired system.
- Wnarray_like
- The critical frequency or frequencies. For lowpass and highpass filters, Wn is a scalar; for bandpass and bandstop filters, Wn is a length-2 sequence. - For a Butterworth filter, this is the point at which the gain drops to 1/sqrt(2) that of the passband (the “-3 dB point”). - For digital filters, if fs is not specified, Wn units are normalized from 0 to 1, where 1 is the Nyquist frequency (Wn is thus in half cycles / sample and defined as 2*critical frequencies / fs). If fs is specified, Wn is in the same units as fs. - For analog filters, Wn is an angular frequency (e.g. rad/s). 
- btype{‘lowpass’, ‘highpass’, ‘bandpass’, ‘bandstop’}, optional
- The type of filter. Default is ‘lowpass’. 
- analogbool, optional
- When True, return an analog filter, otherwise a digital filter is returned. 
- output{‘ba’, ‘zpk’, ‘sos’}, optional
- Type of output: numerator/denominator (‘ba’), pole-zero (‘zpk’), or second-order sections (‘sos’). Default is ‘ba’ for backwards compatibility, but ‘sos’ should be used for general-purpose filtering. 
- fsfloat, optional
- The sampling frequency of the digital system. - Added in version 1.2.0. 
 
- Returns:
- b, andarray, ndarray
- Numerator (b) and denominator (a) polynomials of the IIR filter. Only returned if - output='ba'.
- z, p, kndarray, ndarray, float
- Zeros, poles, and system gain of the IIR filter transfer function. Only returned if - output='zpk'.
- sosndarray
- Second-order sections representation of the IIR filter. Only returned if - output='sos'.
 
 - Notes - The Butterworth filter has maximally flat frequency response in the passband. - The - 'sos'output parameter was added in 0.16.0.- If the transfer function form - [b, a]is requested, numerical problems can occur since the conversion between roots and the polynomial coefficients is a numerically sensitive operation, even for N >= 4. It is recommended to work with the SOS representation.- Warning - Designing high-order and narrowband IIR filters in TF form can result in unstable or incorrect filtering due to floating point numerical precision issues. Consider inspecting output filter characteristics - freqzor designing the filters with second-order sections via- output='sos'.- Examples - Design an analog filter and plot its frequency response, showing the critical points: - >>> from scipy import signal >>> import matplotlib.pyplot as plt >>> import numpy as np - >>> b, a = signal.butter(4, 100, 'low', analog=True) >>> w, h = signal.freqs(b, a) >>> plt.semilogx(w, 20 * np.log10(abs(h))) >>> plt.title('Butterworth filter frequency response') >>> plt.xlabel('Frequency [rad/s]') >>> plt.ylabel('Amplitude [dB]') >>> plt.margins(0, 0.1) >>> plt.grid(which='both', axis='both') >>> plt.axvline(100, color='green') # cutoff frequency >>> plt.show()   - Generate a signal made up of 10 Hz and 20 Hz, sampled at 1 kHz - >>> t = np.linspace(0, 1, 1000, False) # 1 second >>> sig = np.sin(2*np.pi*10*t) + np.sin(2*np.pi*20*t) >>> fig, (ax1, ax2) = plt.subplots(2, 1, sharex=True) >>> ax1.plot(t, sig) >>> ax1.set_title('10 Hz and 20 Hz sinusoids') >>> ax1.axis([0, 1, -2, 2]) - Design a digital high-pass filter at 15 Hz to remove the 10 Hz tone, and apply it to the signal. (It’s recommended to use second-order sections format when filtering, to avoid numerical error with transfer function ( - ba) format):- >>> sos = signal.butter(10, 15, 'hp', fs=1000, output='sos') >>> filtered = signal.sosfilt(sos, sig) >>> ax2.plot(t, filtered) >>> ax2.set_title('After 15 Hz high-pass filter') >>> ax2.axis([0, 1, -2, 2]) >>> ax2.set_xlabel('Time [s]') >>> plt.tight_layout() >>> plt.show() 