According to the following video at 3:50，the man said that by the reason of Fourier series,the f(t) can divided into odd and even part. I understand the function of fourier series,but I still can't figure out.More specific,please!
2026-04-02 15:42:33.1775144553
why analytic signal can separate into odd and even part
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Consider the sum $e(t):=f(t)+f(-t)$. This is obviously an even function ($e(t)=e(-t)$). And consider $o(t):=f(t)-f(-t)$, which is obviously an odd function ($o(t)=-o(-t)$).
Then, $e(t)+o(t)=2f(t)$, so that these two functions define a decomposition of $f$ as the sum of an even and an odd function.
Example: