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Question on Filter implementation #718
Replies: 2 comments 3 replies
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Hi, You can use the forced_response time domain simulation to filter a signal: R = forced_response(Htest, U=x)
y = R.yBut if you are dealing with SISO signals only, there may be no need to include python-control into your dependency stack. You can do everything with Scipy: https://scipy.github.io/devdocs/reference/generated/scipy.signal.lfilter.html#scipy.signal.lfilter: from scipy.signal import lfilter
b = c1*np.array([1, 1])
a = np.array([1, c2])
y = lfilter(b, a, x) |
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@bnavigator , thank you very much, both methods worked well! For me, one advantage of the control version is the nice latex rendering of "H(z)" in the jupyter notebook |
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@bnavigator, one more question on complex coefficients. Is there a way of using the forced_response method to compute Fourier transforms, for instance, to implement a Goertzel algorithm? I get the warning, that the imaginary parts are ignored... Thank you! Hadamard-Zweistein |
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Your forgot a minus sign for the In [13]: H_goertzel = (1-np.exp(-2j*pi*k/N)*z**-1)/(1 -2*np.cos(2*pi*k/N)*z**-1+z**-2)
In [14]: H_goertzel
Out[14]:
In [15]: H_goertzel.num
Out[15]:
[[array([ 1. +0.j , -0.30901699+0.95105652j,
0. +0.j , 0. +0.j ,
0. +0.j ])]]
In [16]: H_goertzel.den
Out[16]: [[array([ 1. , -0.61803399, 1. , 0. , 0. ])]]The coefficients of the transfer function are complex. The resulting fourier transform needs to be complex. We do not support complex valued systems (yet). It has been on the TODO list forever. (see e.g. #484 and the issues linked there). The LaTeX output is wrong here --> You found a bug: #719. The scipy lfilter does what you want: In [17]: lfilter(H_goertzel.num[0][0], H_goertzel.den[0][0], xn)
Out[17]:
array([ 1. +0.j , 4.30901699 +0.95105652j,
9.42705098 +4.39201132j, 14.73606798+10.3228644j ,
19.73606798+17.20477401j]) |
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@bnavigator, ok! Thank you! Looking forward to the complex analysis in control, there is a lot of stuff in classical textbooks, that could be implemented there. "lfilter" seems not so stable, the "control" version may be better. |
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I am interested in using the discrete transfer functions from the control library to filter signals and compute Fourier transforms.
For instance, given a discrete first order butterworth filter
How do I apply "Htest" on a signal "x" in order to obtain the filtered signal? Is there already a feature for that?
Likewise it would be very practical to use the transfer function of the Goertzel alg. to compute a fourier transform of a signal.
Thank you!
Hadamard-Zweistein
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