SciPy

scipy.signal.iirdesign

scipy.signal.iirdesign(wp, ws, gpass, gstop, analog=False, ftype='ellip', output='ba')[source]

Complete IIR digital and analog filter design.

Given passband and stopband frequencies and gains, construct an analog or digital IIR filter of minimum order for a given basic type. Return the output in numerator, denominator (‘ba’) or pole-zero (‘zpk’) form.

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.

ftype : str, optional

The type of IIR filter to design:

  • Butterworth : ‘butter’
  • Chebyshev I : ‘cheby1’
  • Chebyshev II : ‘cheby2’
  • Cauer/elliptic: ‘ellip’
  • Bessel/Thomson: ‘bessel’

output : {‘ba’, ‘zpk’}, optional

Type of output: numerator/denominator (‘ba’) or pole-zero (‘zpk’). Default is ‘ba’.

Returns :

b, a : ndarray, ndarray

Numerator (b) and denominator (a) polynomials of the IIR filter. Only returned if output='ba'.

z, p, k : ndarray, ndarray, float

Zeros, poles, and system gain of the IIR filter transfer function. Only returned if output='zpk'.

See also

butter
Filter design using order and critical points

cheby1, cheby2, ellip, bessel

buttord
Find order and critical points from passband and stopband spec

cheb1ord, cheb2ord, ellipord

iirfilter
General filter design using order and critical frequencies

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