scipy.signal.

buttord#

scipy.signal.buttord(wp, ws, gpass, gstop, analog=False, fs=None)[source]#

Butterworth filter order selection.

Return the order of the lowest order digital or analog Butterworth filter that loses no more than gpass dB in the passband and has at least gstop dB attenuation in the stopband.

Parameters:

wp, wsfloat or array-like

Passband and stopband edge frequencies.

For digital filters, these are in the same units as fs. By default, fs is 2 half-cycles/sample, so these are normalized from 0 to 1, where 1 is the Nyquist frequency. (wp and ws are thus in half-cycles / sample.) For example:

Lowpass: wp = 0.2, ws = 0.3

Highpass: wp = 0.3, ws = 0.2

Bandpass: wp = [0.2, 0.5], ws = [0.1, 0.6]

Bandstop: wp = [0.1, 0.6], ws = [0.2, 0.5]

For analog filters, wp and ws are angular frequencies (e.g., rad/s).

gpassfloat

The maximum loss in the passband (dB).

gstopfloat

The minimum attenuation in the stopband (dB).

analogbool, optional

When True, return an analog filter, otherwise a digital filter is returned.

fsfloat, optional

The sampling frequency of the digital system.

Added in version 1.2.0.

Returns:

ordint: The lowest order for a Butterworth filter which meets specs.
wnndarray or float: The Butterworth natural frequency (i.e. the “3dB frequency”). Should be used with butter to give filter results. If fs is specified, this is in the same units, and fs must also be passed to butter.

See also

butter: Filter design using order and critical points
cheb1ord: Find order and critical points from passband and stopband spec
cheb2ord, ellipord
iirfilter: General filter design using order and critical frequencies
iirdesign: General filter design using passband and stopband spec

Notes

Array API Standard Support

buttord has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

Library	CPU	GPU
NumPy	✅	n/a
CuPy	n/a	✅
PyTorch	✅	✅
JAX	⚠️ no JIT	⛔
Dask	⚠️ computes graph	n/a

The torch backend on GPU does not support the case where wp and ws specify a Bandstop filter.

See Support for the array API standard for more information.

Examples

Design an analog bandpass filter with passband within 3 dB from 20 to 50 rad/s, while rejecting at least -40 dB below 14 and above 60 rad/s. Plot its frequency response, showing the passband and stopband constraints in gray.

>>> from scipy import signal
>>> import matplotlib.pyplot as plt
>>> import numpy as np

>>> N, Wn = signal.buttord([20, 50], [14, 60], 3, 40, True)
>>> b, a = signal.butter(N, Wn, 'band', True)
>>> w, h = signal.freqs(b, a, np.logspace(1, 2, 500))
>>> plt.semilogx(w, 20 * np.log10(abs(h)))
>>> plt.title('Butterworth bandpass filter fit to constraints')
>>> plt.xlabel('Frequency [rad/s]')
>>> plt.ylabel('Amplitude [dB]')
>>> plt.grid(which='both', axis='both')
>>> plt.fill([1,  14,  14,   1], [-40, -40, 99, 99], '0.9', lw=0) # stop
>>> plt.fill([20, 20,  50,  50], [-99, -3, -3, -99], '0.9', lw=0) # pass
>>> plt.fill([60, 60, 1e9, 1e9], [99, -40, -40, 99], '0.9', lw=0) # stop
>>> plt.axis([10, 100, -60, 3])
>>> plt.show()

../../_images/scipy-signal-buttord-1.png