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Determine whether the functions given can be represented by a Fourier series, a) x(t)=cos6t+sin8t+ei2t b) x(t)=cos(t)+sinΠt
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Solution:

(a) x(t)=cos6t+sin8t+ei2t

T1=2Π6=Π3T2=2Π8=Π4T3=2Π/2=ΠT1T2=π/3Π/4=43T1T3=Π/3Π=13

Rational numbers, so periodic, so it can be represented by Fourier series.

 b) x(t)=cost+sinπtT1=2π1=2ΠT2=2ΠΠ=2T1T2=Π

Irrational number, so aperiodic, no Fourier series exist

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