How to approach a "sliding window" integrator response with a low pass filter?

Question

I am simulating an analog system and, at some point, I'm using an ideal "sliding window" integrator which integrates the input analog signal over a well defined time window. I know that I can approach this behaviour with a low-pass filter... Shall I use Butterworth, Chebichev, Bessel? Which order? Specifically, what is the frequency response of the "sliding window" integrator?

Also, I know that the size of the temporal window is inversely proportional to the cut-off frequency of the filter but I don't know exactly what this relation is...

Thank you very much for you help.

Answer 1

An integrator is just a 1st-order pole.

Each of the 3 major types of filters are essentially the same thing when they are reduced to 1st-order implementations.

For the filtering purposes, you will need to implement both a low-pass filter (to prevent aliasing when sampling), and with an integrator in the circuit, you may also need a high-pass filter to eliminate unwanted DC signals that can saturate the integrator.

For a simple 1st-order filter, implemented as a sliding window average, the relation between cutoff frequency (w) and window length (n) is simply w=1/2n.

For translating this into frequencies in Hz, you need to incorporate the sampling rate, and apply 2pi judiciously.

Good luck!