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A functional I encountered before is the Fourier coefficient functional, which I used while studying the Fourier Series. It is defined as
[
F_n(f)=\int_{-\pi}^{\pi} f(x)e^{-inx},dx
]This is a functional because it takes a function (f(x)) as input and returns a complex number as output.
I encountered this in the context of Fourier series, where the goal is to represent a function (or signal) as a sum of sine and cosine waves
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