SciPy

scipy.signal.buttord

scipy.signal.buttord(wp, ws, gpass, gstop, analog=False)[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, ws : float

Passband and stopband edge frequencies. For digital filters, these are normalized from 0 to 1, where 1 is the Nyquist frequency, pi radians/sample. (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).

gpass : float

The maximum loss in the passband (dB).

gstop : float

The minimum attenuation in the stopband (dB).

analog : bool, optional

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

Returns :

ord : int

The lowest order for a Butterworth filter which meets specs.

wn : ndarray or float

The Butterworth natural frequency (i.e. the “3dB frequency”). Should be used with butter to give filter results.

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

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
>>> 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.plot(w, 20 * np.log10(abs(h)))
>>> plt.xscale('log')
>>> plt.title('Butterworth bandpass filter fit to constraints')
>>> plt.xlabel('Frequency [radians / second]')
>>> 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()

(Source code)

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

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