Question

Explain why.

Is Fourier Series can represent any normal, periodic function if we use enough sinusoid term?

Answer 1

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Fourier sereies signal is decomposition of a periodic signal into infinite sum series of sinusoidal harmonics. the fourier series and transformations are useful because we can use them to express original function interms of sinusoidal terms.the fourier series itself periodic function, so the any function that equals to fourier signal must be periodic signal. now we all know in the world periodic as well as normal signals both are existing. a non-periodic function is cannot equal to it's fourier function ,hence it is not useful to use fourier series to analyze normal function.

in other hand , a non periodic function signal that is well behaving expression involving its fourier transform, so it is usefull and allows in terms of sinusoids. the summation of fourier series integration and the resulting equation is inverse fourier transform for a non periodic signal whose frequency is infinite.

yes fourier series can represent any normal,periodic function in sinusoid terms.because the one signal to represent the all kind of periodic and normal signals.