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I am a bit unsure about terminology and method, so I would like to discuss this with anyone who knows anything about this.

I'm examining the properties of a network of parallel capacitors. I have calculated an impedance versus frequency curve, Z(f), using complex impedance of the capacitors capacitance, inductance and resistance (using octave and the Frequency Domain Target Impedance method (FDTI)). The next property I would like to examine is the step response to a 1 ampere step of this filter(correct term?), with a 0.8 ns 10%-90% rise time. This would give me a voltage as a function of time, v(t). The actual property I want to know is how the system responds (in volts) to a number of digital switches that turns on and together sinks 1 ampere.

If I understand this correctly, the way to do this is to create a step function,i(t), with the specified properties and make a fourier transform of this, I(f). Next step would be multiplying I(f) and Z(f), to get V(f). By doing an inverse fast fourier transform of this, I would get the step response voltage, v(t).

Assuming my reasoning is correct, what would be the best i(t) to use? A Heaviside step function seems to be impractical to use on an actual, physical system. If understand this correctly, a gaussian step would be practical and close to the actual physical step?

Is the method I'm describing correct, and if so, does it have a name so that I can look it up in the litterature? What I'm looking for is a method for actually calculating v(t) mainly using fft and ifft, not doing a mathematical model.

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# Voltage step response of impedance frequency response

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