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ParametersReturnsBackRef

Parameters

wp, ws : float

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).

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.

fs : float, optional

The sampling frequency of the digital system.

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. 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

iirdesign

General filter design using passband and stopband spec

iirfilter

General filter design using order and critical frequencies

Examples

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 [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()

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