# Compensating integrator filter

1. Sep 23, 2010

### divB

Hi,

I have a signal $$f(t)$$ with nyquist rate W, i.e. the maximum frequency is W/2.

This signal is filtered with an integrator (simulated in Simulink) the following way:

$$f_I(t) = \int_t^{t+\frac{1}{W}} f(t)\,dt$$

In words: I integrate the signal for a period of 1/W, then the integrator is reset. It is obvious that the signal won't be the same afterwards; however I only integrate for 1/nyquistrate long. So I think it should be possible to compensate this filter in digital domain.

But: How? This is a lowpass first order. I tried to get the transfer function which should be something like (1+z^-1) and filter with the reverse, i.e. 1/(1+z^-1). But this filter is unstable and the results therefore unuseble.

Does anybody know how I could compensate this filter in digital domain (when I have the nyquist samples of $$f_I(t)$$)?

Regards, divB

PS: The whole thing should be equivalent to oversample $$f(t)$$ with a factor of e.g. 100, that is, the sampling rate is W*100; and afterwards summing up 100 consecutive samples in digital domain ...