# Remove AC component from the mixed signal using an elliptic filter

I have a signal like this:

$$s(t) = C + a \cdot sin(2 \cdot \pi \cdot f \cdot t)$$

where $$C$$ - arbitrary constant, $$f$$ - frequency of AC component (Hz) and $$a$$ - amplitude of AC component.

Parameters: $$C = 1$$, $$f = 1$$, and $$a = 0.1$$.

I want to synthesize a filter that will remove AC component with an angular frequency $$\omega = 2 \cdot \pi \cdot f$$ from this signal, i.e.:

$$s(t) = C + a \cdot sin(2 \cdot \pi \cdot f \cdot t) \xrightarrow{After Filtering} s(t) ≈ C$$

It is difficult to make this ideal, therefore, an elliptic filter was chosen as a filter, as a good frequency splitter.

After tuning it, I get the following frequency response of the filter:

The model of a computational experiment is as follows:

And the following results are obtained.

AC component has not been deleted. Signal after the filter repeats the input. In theory, AC components with a frequency above 0.5 Hz (and in my case the frequency is 1 Hz) should be removed, and only the constant $$C$$ component should remain, i.e. $$1$$.

Where did I make a mistake?

I agree, the 1 Hz signal should be attenuated given the filter response. I suggest sweeping the input frequency to create the frequency response manually as I assume the filter was somehow scaled, possibly by not including a factor of $$T$$ in the mapping from the analog filter. Try a much higher frequency to see where it is nulled and then narrow in on the actual cut-off.