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?