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 > _How can we extract a DC signal from a mixed signal?_

You use a low-pass filter with a cut-off frequency that is significantly lower than your lowest AC signal frequency. If you need better filtering use a higher order low-pass filter. If you need both fast response to the DC level and high AC rejection you may never be able to achieve what you want.

However, your question sounds like an XY problem so, it might be better if you explain precisely what you are trying to achieve.