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I wanted to have a little clarification about this line in relation to Fourier Series: (It's about a periodic and symmetrical signal)

"x(t) is a periodic signal. As cos nwt is an even function and sin nwt is an odd function. So, if x(t) is an even function of t, then x(t) cos nwt is also an even function and x(t) sn nwt is an odd function of t.

Similarly, if x(t) is an odd function of t, then x(t) cos nwt is an odd function of t and x(t) sin nwt is an even function of t."

- Linear Signal & Systems, B.P Lathi.

x(t) is both cos and sin functions multiplied right? And isn't it that an when an even function is multiplied with an odd function, we get an odd function? So how can be x(t) even? (as in the above excerpt)

Thanks.

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# Question about Fourier Series (symmetrical signals)

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