Let's say I have a P that depends on t: P(t). I also have function C, which depends on P(t) and indirectly on t: C(P(t), t). I know that the Fourier Transform of P(t) would be P(w). What would be the transformation of C in general to the frequency domain? (Note: I am looking for the general case where the dependence of C on P has not been defined.... is there any mathematical relation to taking the Fourier transform of C)?
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You will run into complications just from the composition (i.e. even if $C = C(P(t))$ is independent of $t$). See this great answer: https://math.stackexchange.com/a/803458/586016 – cohomonoid Jan 21 '22 at 16:43