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Any periodic function f(t), with a fundamental angular frequency wo, can be represented by the sum of a constant and a series of sine

 

Any periodic function f(t), with a fundamental angular frequency wo, can be represented by the sum of a constant and a series of sine and cosine waves. In symbolic form, this is written as, f(t)= a + a coswot + a cos 2wot ++a, cos nwot + bn sin noot + b sin wot + b sin 2wot + ..** (1) The constant a, is simply the time average of the function over the period T. This can be evaluated from The constant a, can be evaluated from, = f(t) dt an = f(t) cos(nwot) dt And, the constant b, can be evaluated from, bn=ff(t) sin(not) dt (2) O The Eq. (1) above is an infinite series, so the constant a and b can only be determined for a limited number of terms (n).

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