group_delay(system, w=512, whole=False, fs=6.283185307179586)
The group delay measures by how many samples amplitude envelopes of various spectral components of a signal are delayed by a filter. It is formally defined as the derivative of continuous (unwrapped) phase:
d jw
D(w) = - -- arg H(e)
dw
The similar function in MATLAB is called :None:None:`grpdelay`.
If the transfer function $H(z)$ has zeros or poles on the unit circle, the group delay at corresponding frequencies is undefined. When such a case arises the warning is raised and the group delay is set to 0 at those frequencies.
For the details of numerical computation of the group delay refer to .
Numerator and denominator coefficients of a filter transfer function.
If a single integer, then compute at that many frequencies (default is N=512).
If an array_like, compute the delay at the frequencies given. These are in the same units as :None:None:`fs`.
Normally, frequencies are computed from 0 to the Nyquist frequency, fs/2 (upper-half of unit-circle). If :None:None:`whole` is True, compute frequencies from 0 to fs. Ignored if w is array_like.
The sampling frequency of the digital system. Defaults to 2*pi radians/sample (so w is from 0 to pi).
The frequencies at which group delay was computed, in the same units as :None:None:`fs`. By default, w is normalized to the range [0, pi) (radians/sample).
The group delay.
Compute the group delay of a digital filter.
freqz
Frequency response of a digital filter
>>> from scipy import signal
... b, a = signal.iirdesign(0.1, 0.3, 5, 50, ftype='cheby1')
... w, gd = signal.group_delay((b, a))
>>> import matplotlib.pyplot as plt
... plt.title('Digital filter group delay')
... plt.plot(w, gd)
... plt.ylabel('Group delay [samples]')
... plt.xlabel('Frequency [rad/sample]')
... plt.show()
The following pages refer to to this document either explicitly or contain code examples using this.
scipy.signal._fir_filter_design.minimum_phase
scipy.signal._filter_design.group_delay
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