Yes you have advanced math... You pretty much write just that..
More background. The question just came into my mind when I saw yet another Bodnar trace:
Is it possible to display the frequency response
directly with a math function, if the stimulus is an (almost ideal) square wave from a Bodnar pulser?
The fourier spectrum of an ideal 10MHz square wave is a comb, with teeth at 10, 30, 50,... MHz (-> classical square wave harmonics).
The magnitude of the teeth follows a 1/f response. Multiplication of each tooth by its frequency would therefore result in a "flat comb", with teeth of equal height.
It the spectrum of the stimulus is a "flat comb", then the deviation of the tips from a horizontal line (after the frontend) reflects the frequency response.
Since it is a linear system, the frequency-dependent scaling of the stimulus spectrum can also be done after the DUT.
This leads to the following 4 approaches, and I wonder which of them could be realized via supported math expressions:
FFT(X) * f [i.e.multiplication of each frequency bin by its freqency, in linear space, not dB]
FFT(X) * Y [where Y is a constant, pre-defined, "hand-crafted" frequency domain trace, and the multiplication happens in linear space]
FFT(X) + Z [where Z is a constant, pre-defined frequency domain trace in dB, and the addition happens in dB space]
FFT(dX/dt) [since multiplication by frequency in the frequency domain is equivalent to differentiation in the time domain]
Potential sources of inaccuracy/untertainty are still:
* potential aliasing (if >= 1GHz is not yet sufficiently attenuated)
* The exact implementatin of dX/dt is not known, and it is supposed to be a numeric approximation
* Bodnar pulse is fast, but still not an ideal rectangle, so the stimulus spectrum already has a small a priori roll-off from the ideal 1/f comb spectrum in the region of interest