scipy.signal.cheby1#
- scipy.signal.cheby1(N, rp, Wn, btype='low', analog=False, output='ba', fs=None)[source]#
Chebyshev type I digital and analog filter design.
Design an Nth-order digital or analog Chebyshev type I filter and return the filter coefficients.
- Parameters:
- Nint
The order of the filter.
- rpfloat
The maximum ripple allowed below unity gain in the passband. Specified in decibels, as a positive number.
- Wnarray_like
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 -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’.
- analogbool, 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.
- fsfloat, optional
The sampling frequency of the digital system.
New in version 1.2.0.
- Returns:
- b, andarray, ndarray
Numerator (b) and denominator (a) polynomials of the IIR filter. Only returned if
output='ba'
.- z, p, kndarray, ndarray, float
Zeros, poles, and system gain of the IIR filter transfer function. Only returned if
output='zpk'
.- sosndarray
Second-order sections representation of the IIR filter. Only returned if
output='sos'
.
Notes
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.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.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()