Let's say you have a signal that relatively slowly rises from 0 to 1, then suddenly from one sample to the next drops back to 0, creating a sharp discontinuity. Let's say you run it through a one pole low pass filter at a given frequency, say 200 Hz to smooth it.

Is there any way to predict or graph or calculate how long it will take after the discontinuity for the signal to reach 0 or near 0?

  • $\begingroup$ there's no "discontinuity" or "continuity" in discrete signals; a sudden change is just that, a high-bandwidth event. Are you perhaps looking for that filter's step response? $\endgroup$ – Marcus Müller Dec 29 '19 at 11:43
  • $\begingroup$ Yes thank you - "step response" is the right term for it. That was helpful to learn that phrase. I did not know that's what it's called. Hilmar answered the rest of my question. $\endgroup$ – mike Dec 29 '19 at 19:08

Infinitely long. It's an exponential decay, so it never goes back to 0.

The time constant for a 200 Hz filter is $\frac{1}{2 \pi f} \approx 0.8ms $. About every 0.8ms it drops by about $2/3$ or every 1.84 ms it drops by a factor of 10.

If you define "almost zero" as one millionths you need to wait $6*1.8ms$ or about 11ms.

  • $\begingroup$ Oh wow Hilmar. I didn't know that. That's very helpful. So are you saying time to $1/e$ amplitude for a one pole low pass filter when given a discontinuity is $1/(2*pi*f)$? That's what I needed to know. $\endgroup$ – mike Dec 29 '19 at 18:56

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