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Module « scipy.signal »

Fonction iirdesign - module scipy.signal

Signature de la fonction iirdesign

def iirdesign(wp, ws, gpass, gstop, analog=False, ftype='ellip', output='ba', fs=None) 

Description

help(scipy.signal.iirdesign)

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'), pole-zero ('zpk') or second order
sections ('sos') form.

Parameters
----------
wp, ws : float or array like, shape (2,)
    Passband and stopband edge frequencies. Possible values are scalars
    (for lowpass and highpass filters) or ranges (for bandpass and bandstop
    filters).
    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. 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).
    Note, that for bandpass and bandstop filters passband must lie strictly
    inside stopband or vice versa. Also note that the cutoff at the band edges 
    for IIR filters is defined as half-power, so -3dB, not half-amplitude (-6dB)
    like for `scipy.signal.fiwin`.
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'

output : {'ba', 'zpk', 'sos'}, optional
    Filter form of the output:

        - second-order sections (recommended): 'sos'
        - numerator/denominator (default)    : 'ba'
        - pole-zero                          : 'zpk'

    In general the second-order sections ('sos') form  is
    recommended because inferring the coefficients for the
    numerator/denominator form ('ba') suffers from numerical
    instabilities. For reasons of backward compatibility the default
    form is the numerator/denominator form ('ba'), where the 'b'
    and the 'a' in 'ba' refer to the commonly used names of the
    coefficients used.

    Note: Using the second-order sections form ('sos') is sometimes
    associated with additional computational costs: for
    data-intense use cases it is therefore recommended to also
    investigate the numerator/denominator form ('ba').

fs : float, optional
    The sampling frequency of the digital system.

    .. versionadded:: 1.2.0

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'``.
sos : ndarray
    Second-order sections representation of the IIR filter.
    Only returned if ``output='sos'``.

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

Notes
-----
The ``'sos'`` output parameter was added in 0.16.0.

Examples
--------
>>> import numpy as np
>>> from scipy import signal
>>> import matplotlib.pyplot as plt
>>> import matplotlib.ticker

>>> wp = 0.2
>>> ws = 0.3
>>> gpass = 1
>>> gstop = 40

>>> system = signal.iirdesign(wp, ws, gpass, gstop)
>>> w, h = signal.freqz(*system)

>>> fig, ax1 = plt.subplots()
>>> ax1.set_title('Digital filter frequency response')
>>> ax1.plot(w, 20 * np.log10(abs(h)), 'b')
>>> ax1.set_ylabel('Amplitude [dB]', color='b')
>>> ax1.set_xlabel('Frequency [rad/sample]')
>>> ax1.grid(True)
>>> ax1.set_ylim([-120, 20])
>>> ax2 = ax1.twinx()
>>> phase = np.unwrap(np.angle(h))
>>> ax2.plot(w, phase, 'g')
>>> ax2.set_ylabel('Phase [rad]', color='g')
>>> ax2.grid(True)
>>> ax2.axis('tight')
>>> ax2.set_ylim([-6, 1])
>>> nticks = 8
>>> ax1.yaxis.set_major_locator(matplotlib.ticker.LinearLocator(nticks))
>>> ax2.yaxis.set_major_locator(matplotlib.ticker.LinearLocator(nticks))

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