SciPy

scipy.signal.ellipord

scipy.signal.ellipord(wp, ws, gpass, gstop, analog=False)[source]

Elliptic (Cauer) filter order selection.

Return the order of the lowest order digital or analog elliptic 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 an Elliptic (Cauer) filter that meets specs.

wn : ndarray or float

The Chebyshev natural frequency (the “3dB frequency”) for use with ellip to give filter results.

See also

ellip
Filter design using order and critical points
buttord
Find order and critical points from passband and stopband spec

cheb1ord, cheb2ord

iirfilter
General filter design using order and critical frequencies
iirdesign
General filter design using passband and stopband spec

Examples

Design an analog highpass filter such that the passband is within 3 dB above 30 rad/s, while rejecting -60 dB at 10 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.ellipord(30, 10, 3, 60, True)
>>> b, a = signal.ellip(N, 3, 60, Wn, 'high', True)
>>> w, h = signal.freqs(b, a, np.logspace(0, 3, 500))
>>> plt.plot(w, 20 * np.log10(abs(h)))
>>> plt.xscale('log')
>>> plt.title('Elliptical highpass filter fit to constraints')
>>> plt.xlabel('Frequency [radians / second]')
>>> plt.ylabel('Amplitude [dB]')
>>> plt.grid(which='both', axis='both')
>>> plt.fill([.1, 10,  10,  .1], [1e4, 1e4, -60, -60], '0.9', lw=0) # stop
>>> plt.fill([30, 30, 1e9, 1e9], [-99,  -3,  -3, -99], '0.9', lw=0) # pass
>>> plt.axis([1, 300, -80, 3])
>>> plt.show()

(Source code)

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

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