Question
In Fourier Series, to calculate the harmonics of a periodic function, the following identities are considered: (see image) Suppose T = 2 and f(t)= t
In Fourier Series, to calculate the harmonics of a periodic function, the following identities are considered: (see image) Suppose T = 2 and f(t)= t between [-T/2,T\2]. Also remember that w0 = 2pi/T and where n ? Z^+ is requested ? Analyze the nature of the function f (t), as well as the trigonometric functions involved, taking into account that - The integral of an odd function is zero. - The integral of an even function is twice the evaluated function. - The product of two even functions is even. - The product of two odd functions is even. - The product of an even and an odd function is odd. Based on the requested analysis, give solid arguments to indicate: - If it is necessary to calculate in a developed way the 3 integrals. - If it is necessary to calculate in a developed way 2 of them and indicate which ones. - If it is necessary to calculate only one of them in a developed way and indicate which one. ? Based on the previous analysis, calculate the corresponding integrals.
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