How are signals added or decomposed in an electronic circuit?

I learn about signal processing but couldn't find what hardware or circuit elements actually used to physically add or decompose new forms. For example lest say I want to add a sinusoid signal which is 2 GHz with another sinusoid with 1 GHz. How do they implement this in a circuit? (I also wonder how they... show more I learn about signal processing but couldn't find what hardware or circuit elements actually used to physically add or decompose new forms. For example lest say I want to add a sinusoid signal which is 2 GHz with another sinusoid with 1 GHz. How do they implement this in a circuit? (I also wonder how they decompose signals to their sinusoid components). Could you give me some introductory explanation or keywords.
Thanks in advance,
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