bundles / scipy latest / scipy / signal / _filter_design / iircomb

function

`scipy.signal._filter_design:iircomb`

source: /scipy/signal/_filter_design.py :5626

Signature

   def     iircomb (    w0    ,    Q    ,    ftype    =  notch   ,    fs    =  2.0   ,  * ,     pass_zero    =  False   ,    xp    =  None   ,    device    =  None     )

Summary

Design IIR notching or peaking digital comb filter.

Extended Summary

A notching comb filter consists of regularly-spaced band-stop filters with a narrow bandwidth (high quality factor). Each rejects a narrow frequency band and leaves the rest of the spectrum little changed.

A peaking comb filter consists of regularly-spaced band-pass filters with a narrow bandwidth (high quality factor). Each rejects components outside a narrow frequency band.

Parameters

w0 : float: The fundamental frequency of the comb filter (the spacing between its peaks). This must evenly divide the sampling frequency. If fs is specified, this is in the same units as fs. By default, it is a normalized scalar that must satisfy 0 < w0 < 1, with w0 = 1 corresponding to half of the sampling frequency.
Q : float: Quality factor. Dimensionless parameter that characterizes notch filter -3 dB bandwidth bw relative to its center frequency, Q = w0/bw.
ftype : {'notch', 'peak'}: The type of comb filter generated by the function. If 'notch', then the Q factor applies to the notches. If 'peak', then the Q factor applies to the peaks. Default is 'notch'.
fs : float, optional: The sampling frequency of the signal. Default is 2.0.
pass_zero : bool, optional: If False (default), the notches (nulls) of the filter are centered on frequencies [0, w0, 2*w0, ...], and the peaks are centered on the midpoints [w0/2, 3*w0/2, 5*w0/2, ...]. If True, the peaks are centered on [0, w0, 2*w0, ...] (passing zero frequency) and vice versa.
versionadded 1.9.0
xp : array_namespace, optional: Optional array namespace. Should be compatible with the array API standard, or supported by array-api-compat. Default: numpy
device: any: optional device specification for output. Should match one of the supported device specification in xp.

Returns

b, a : ndarray, ndarray: Numerator (b) and denominator (a) polynomials of the IIR filter.

Raises

: ValueError: If w0 is less than or equal to 0 or greater than or equal to fs/2, if fs is not divisible by w0, if ftype is not 'notch' or 'peak'

Notes

For implementation details, see ^[1]. The TF implementation of the comb filter is numerically stable even at higher orders due to the use of a single repeated pole, which won't suffer from precision loss.

Array API Standard Support

iircomb has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

====================  ====================  ====================
Library               CPU                   GPU
====================  ====================  ====================
NumPy                 ✅                     n/a                 
CuPy                  n/a                   ✅                   
PyTorch               ✅                     ✅                   
JAX                   ⛔                     ⛔                   
Dask                  ✅                     n/a                 
====================  ====================  ====================

See dev-arrayapi for more information.

Examples

Design and plot notching comb filter at 20 Hz for a signal sampled at 200 Hz, using quality factor Q = 30

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

✓

fs = 200.0  # Sample frequency (Hz)
f0 = 20.0  # Frequency to be removed from signal (Hz)
Q = 30.0  # Quality factor
b, a = signal.iircomb(f0, Q, ftype='notch', fs=fs)

✓

freq, h = signal.freqz(b, a, fs=fs)
response = abs(h)
response[response == 0] = 1e-20
fig, ax = plt.subplots(2, 1, figsize=(8, 6), sharex=True)

✓

ax[0].plot(freq, 20*np.log10(abs(response)), color='blue')
ax[0].set_title("Frequency Response")
ax[0].set_ylabel("Amplitude [dB]", color='blue')
ax[0].set_xlim([0, 100])
ax[0].set_ylim([-30, 10])

✗

ax[0].grid(True)

✓

ax[1].plot(freq, np.mod(np.angle(h, deg=True) + 180, 360) - 180, color='green')
ax[1].set_ylabel("Phase [deg]", color='green')
ax[1].set_xlabel("Frequency [Hz]")
ax[1].set_xlim([0, 100])
ax[1].set_yticks([-90, -60, -30, 0, 30, 60, 90])
ax[1].set_ylim([-90, 90])

✗

ax[1].grid(True)
plt.show()

✓

Design and plot peaking comb filter at 250 Hz for a signal sampled at 1000 Hz, using quality factor Q = 30

fs = 1000.0  # Sample frequency (Hz)
f0 = 250.0  # Frequency to be retained (Hz)
Q = 30.0  # Quality factor
b, a = signal.iircomb(f0, Q, ftype='peak', fs=fs, pass_zero=True)

✓

freq, h = signal.freqz(b, a, fs=fs)
response = abs(h)
response[response == 0] = 1e-20
fig, ax = plt.subplots(2, 1, figsize=(8, 6), sharex=True)

✓

ax[0].plot(freq, 20*np.log10(np.maximum(abs(h), 1e-5)), color='blue')
ax[0].set_title("Frequency Response")
ax[0].set_ylabel("Amplitude [dB]", color='blue')
ax[0].set_xlim([0, 500])
ax[0].set_ylim([-80, 10])

✗

ax[0].grid(True)

✓

ax[1].plot(freq, np.mod(np.angle(h)*180/np.pi + 180, 360) - 180, color='green')
ax[1].set_ylabel("Phase [deg]", color='green')
ax[1].set_xlabel("Frequency [Hz]")
ax[1].set_xlim([0, 500])
ax[1].set_yticks([-90, -60, -30, 0, 30, 60, 90])
ax[1].set_ylim([-90, 90])

✗

ax[1].grid(True)
plt.show()

✓

Aliases

scipy.signal.iircomb