I have seen many times the analogy that the High Pass Filter (HPF) is a differentiator, something that explains some interesting facts, like that a non-negative signal might have negative components as in the case of differentiating a positive signal.
1) Is there an equivalent analogy for the LPF? How about the BPF?
1) Is there a mathematical formulation that prove these results?
Best Answer
The corollary is an integrator for a LPF. If you have a resistor feeding into a capacitor, then you get your input signal from the beginning of time integrated up to now.
Here's the math behind what I describe.
Band pass would be a LPF + a HPF so potentially an integrator feeding into a differentiator.