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Module « scipy.signal »

Fonction ellip - module scipy.signal

Signature de la fonction ellip

def ellip(N, rp, rs, Wn, btype='low', analog=False, output='ba', fs=None) 

Description

help(scipy.signal.ellip)

Elliptic (Cauer) digital and analog filter design.

Design an Nth-order digital or analog elliptic filter and return
the filter coefficients.

Parameters
----------
N : int
    The order of the filter.
rp : float
    The maximum ripple allowed below unity gain in the passband.
    Specified in decibels, as a positive number.
rs : float
    The minimum attenuation required in the stop band.
    Specified in decibels, as a positive number.
Wn : array_like
    A scalar or length-2 sequence giving the critical frequencies.
    For elliptic filters, this is the point in the transition band at
    which the gain first drops below -`rp`.

    For digital filters, `Wn` 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. (`Wn` is thus in
    half-cycles / sample.)

    For analog filters, `Wn` is an angular frequency (e.g., rad/s).
btype : {'lowpass', 'highpass', 'bandpass', 'bandstop'}, optional
    The type of filter. Default is 'lowpass'.
analog : bool, optional
    When True, return an analog filter, otherwise a digital filter is
    returned.
output : {'ba', 'zpk', 'sos'}, optional
    Type of output:  numerator/denominator ('ba'), pole-zero ('zpk'), or
    second-order sections ('sos'). Default is 'ba' for backwards
    compatibility, but 'sos' should be used for general-purpose filtering.
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
--------
ellipord, ellipap

Notes
-----
Also known as Cauer or Zolotarev filters, the elliptical filter maximizes
the rate of transition between the frequency response's passband and
stopband, at the expense of ripple in both, and increased ringing in the
step response.

As `rp` approaches 0, the elliptical filter becomes a Chebyshev
type II filter (`cheby2`). As `rs` approaches 0, it becomes a Chebyshev
type I filter (`cheby1`). As both approach 0, it becomes a Butterworth
filter (`butter`).

The equiripple passband has N maxima or minima (for example, a
5th-order filter has 3 maxima and 2 minima). Consequently, the DC gain is
unity for odd-order filters, or -rp dB for even-order filters.

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

Examples
--------
Design an analog filter and plot its frequency response, showing the
critical points:

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

>>> b, a = signal.ellip(4, 5, 40, 100, 'low', analog=True)
>>> w, h = signal.freqs(b, a)
>>> plt.semilogx(w, 20 * np.log10(abs(h)))
>>> plt.title('Elliptic filter frequency response (rp=5, rs=40)')
>>> plt.xlabel('Frequency [rad/s]')
>>> plt.ylabel('Amplitude [dB]')
>>> plt.margins(0, 0.1)
>>> plt.grid(which='both', axis='both')
>>> plt.axvline(100, color='green') # cutoff frequency
>>> plt.axhline(-40, color='green') # rs
>>> plt.axhline(-5, color='green') # rp
>>> plt.show()

Generate a signal made up of 10 Hz and 20 Hz, sampled at 1 kHz

>>> t = np.linspace(0, 1, 1000, False)  # 1 second
>>> sig = np.sin(2*np.pi*10*t) + np.sin(2*np.pi*20*t)
>>> fig, (ax1, ax2) = plt.subplots(2, 1, sharex=True)
>>> ax1.plot(t, sig)
>>> ax1.set_title('10 Hz and 20 Hz sinusoids')
>>> ax1.axis([0, 1, -2, 2])

Design a digital high-pass filter at 17 Hz to remove the 10 Hz tone, and
apply it to the signal. (It's recommended to use second-order sections
format when filtering, to avoid numerical error with transfer function
(``ba``) format):

>>> sos = signal.ellip(8, 1, 100, 17, 'hp', fs=1000, output='sos')
>>> filtered = signal.sosfilt(sos, sig)
>>> ax2.plot(t, filtered)
>>> ax2.set_title('After 17 Hz high-pass filter')
>>> ax2.axis([0, 1, -2, 2])
>>> ax2.set_xlabel('Time [s]')
>>> plt.tight_layout()
>>> plt.show()

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