New answers tagged complex
2
Why not just implement a complex notch filter as described on page 20 of these notes.
This gives the following frequency response.
You might want to change the 0.9 figure to something closer to 1. And I'm not clear on what the frequency you're trying to knock out is.
Code below
Full Jupyter Notebook here.
# Page 20 of https://courses.engr.illinois.edu/...
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Here is one way to design a complex notch IIR filter
Start with a real IIR filter, determine poles, zeros and gain
Remove all the poles and zeros at negative frequencies, take the root of the gain
Turn back into polynomials and run as a complex filter.
I don't know whether scipy.signal.iirfilter() supports complex filter coefficients, but Matlab's filter() ...
3
any real-valued system, such as a filter as yours, is symmetrical in spectrum. So, what you observe is inevitable. This is kind of a direct result from the fact that real signals are always symmetrical in spectrum, and a real system can't make a complex signal out of a real signal.
If you need a one-sided filter, it needs to be complex. So, instead of ...
2
For what values of the model parameters, does it generate a real signal?
That's probably not possible. Roughly speaking, your frequencies are all positive and a real signal must have a conjugate symmetric spectrum, i.e. equal amount of positive and negative frequencies.
If you make the sum run from $-K$ to $+K$ and set $a_k = a_{-k}, \alpha_k = \alpha_{-k}, ...
1
There are two interpretations of this problem.
One is that only real voltages and currents can exist in the real world. Complex signals exist to simplify calculations, and in the DSP realm, where computers can easily handle complex numbers.
The other interpretation is that a complex signal is just two real signals, one of which is labeled "imaginary&...
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