Do I use the absolute-value of the FFT frequencies when using the Laplace equations for calculating the impedance of an RLC circuit?

I'm currently working on something where I need to numerically analyze the steady-state response of an RLC circuit. I'm starting with an almost-square wave (i.e. the output me arbitrary waveform generator can achieve plus the frequency response of the amplifier) which I then converted to the frequency domain with scipy's FFT.

I then use numpy.fft.fftfreq to get the frequencies of that FFT result, so at this point I have the frequencies and their corresponding powers. (Note that I'm not doing any normalization yet because the absolute amplitudes here don't matter much and the only thing I'm going to do later is pass it through an IFFT to get the time-domain signal).

So then comes the RLC circuit. I'm using the Laplace equations (R, sL, 1/sC) to calculate the impedance.

And now I have an issue which I can't seem to find a reference to online: when I calculate those, do I use the absolute value of the frequency array? Or do I use the negative frequencies? Or do I trim out all the negative frequencies?

Obviously, if I use the negative frequencies, resonance becomes... tricky, to put it mildly.


1 Answer 1


Laplace and Fourier transforms of real circuits/signals are symmetrical around zero frequency. Asymmetry is observed only with complex circuits/signals. That said, unless we can see the full calculations you're doing, it's difficult to explain exactly how to apply them.


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