when calculating the maximum square error I have this formula $$E^* = \int_{-\pi}^{\pi}f^2 dx - \pi \left[ 2a_0^2 + \sum_{n = 1}^N (a_n^2 + b_n^2) \right ]$$ But I was wondering, if I have a complex fourier series, can I just exchange $a_n$ & $b_n$ with $c_n$ like this $$E^* = \int_{-\pi}^{\pi}f^2 dx - \pi \left[ 2a_0^2 + \sum_{n = 1}^N c_n^2 \right ]$$
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What are $a_n,b_n,c_n$? – copper.hat Sep 19 '17 at 14:56
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$a_n,b_n$ are the fourier coefficients. $c_n$ is the complex fourier coefficient. – Viktor Sep 19 '17 at 14:58
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Is there some relationship between the $a_n,b_n,c_n$??? If you set $c_n = \sqrt{a_n^2+b_n^2}$ then you can replace the $a_n,b_n$. It is really not clear what you are asking. – copper.hat Sep 19 '17 at 14:59