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:

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The model of a computational experiment is as follows:

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And the following results are obtained.

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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?


1 Answer 1


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.

Further notice that the frequency response is not completely nulled at 1 Hz, but would have about 65 dB attenuation and that it also contributes significant phase distortion to the passband.

Instead of using an elliptic lowpass filter, consider using a 2nd order notch filter for eliminating AC signals. This implementation is detailed further at this post:

Transfer function of second order notch filter


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