cheby1(N, rp, Wn, btype='low', analog=False, output='ba', fs=None)
Design an Nth-order digital or analog Chebyshev type I filter and return the filter coefficients.
The Chebyshev type I filter maximizes the rate of cutoff between the frequency response's passband and stopband, at the expense of ripple in the passband and increased ringing in the step response.
Type I filters roll off faster than Type II (cheby2
), but Type II filters do not have any ripple in the passband.
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.
The order of the filter.
The maximum ripple allowed below unity gain in the passband. Specified in decibels, as a positive number.
A scalar or length-2 sequence giving the critical frequencies. For Type I filters, this is the point in the transition band at which the gain first drops below -:None:None:`rp`.
For digital filters, :None:None:`Wn` are in the same units as :None:None:`fs`. By default, :None:None:`fs` is 2 half-cycles/sample, so these are normalized from 0 to 1, where 1 is the Nyquist frequency. (:None:None:`Wn` is thus in half-cycles / sample.)
For analog filters, :None:None:`Wn` is an angular frequency (e.g., rad/s).
The type of filter. Default is 'lowpass'.
When True, return an analog filter, otherwise a digital filter is returned.
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.
The sampling frequency of the digital system.
Numerator (b) and denominator (a) polynomials of the IIR filter. Only returned if output='ba'
.
Zeros, poles, and system gain of the IIR filter transfer function. Only returned if output='zpk'
.
Second-order sections representation of the IIR filter. Only returned if output=='sos'
.
Chebyshev type I digital and analog filter design.
Design an analog filter and plot its frequency response, showing the critical points:
>>> from scipy import signal
... import matplotlib.pyplot as plt
>>> b, a = signal.cheby1(4, 5, 100, 'low', analog=True)
... w, h = signal.freqs(b, a)
... plt.semilogx(w, 20 * np.log10(abs(h)))
... plt.title('Chebyshev Type I frequency response (rp=5)')
... plt.xlabel('Frequency [radians / second]')
... plt.ylabel('Amplitude [dB]')
... plt.margins(0, 0.1)
... plt.grid(which='both', axis='both')
... plt.axvline(100, color='green') # cutoff frequency
... 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 15 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.cheby1(10, 1, 15, 'hp', fs=1000, output='sos')
... filtered = signal.sosfilt(sos, sig)
... ax2.plot(t, filtered)
... ax2.set_title('After 15 Hz high-pass filter')
... ax2.axis([0, 1, -2, 2])
... ax2.set_xlabel('Time [seconds]')
... plt.tight_layout()
... plt.show()
The following pages refer to to this document either explicitly or contain code examples using this.
scipy.signal._filter_design.ellip
scipy.signal._filter_design.iirfilter
scipy.signal._filter_design.cheb1ap
scipy.signal._filter_design.cheby2
scipy.signal._filter_design.cheb1ord
scipy.signal._filter_design.cheby1
scipy.signal._filter_design.iirdesign
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