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'.

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