I have the following function $$\left|a_0 + \sum_{m=1}^{\infty}A_m \cos(mx)\right|$$ Is there any way to rewrite such an equation as $$\left|B_0\right| + \sum_{m=1}^{\infty}\left|B_m\cos(mx)\right|$$ or something similar?
modulus of fourier series
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summation
fourier-series
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0You can apply triangle inequality to get that: $$|a_0+\sum_{m = 1}^\infty A_m\cos(mx)|\leq |B_0|+\sum_{m = 1}^\infty |B_m\cos(mx)|$$ Generically, you can't expect to do better than this. – 2017-01-17
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0What do you mean by "modulus". It seems you want to simplify $\lvert a(x) \rvert$. – 2017-01-17
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0I would like to split the absolute value into many absolute values applied to each of the terms in the summation separately. I know this is no rule but I thought that maybe for sinusoids there would have been some rule (I am no mathematician though). – 2017-01-17