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(Solved): Given the following periodic waveform with period T=6,f(t)={(20,-1<=t<=1),(0,1<=t<5):}. ...
Given the following periodic waveform with period
T=6,f(t)={(20,-1<=t<=1),(0,1<=t<5):}. (a) Find the symmetry: Odd only Odd and half-wave Even and half wave No symmetry Half wave only Even only (b) Calculate
a_(0)and
w_(0)才
a_(0)=,;,\omega _(0)=Express
a_(0)to 3 significant digits and give the exact value for
\omega _(0). Type Pi for
\pi . (c) Which of the following is the Fourier Series expansion for the given function? (zero harmonics are omitted).
b_(1)sin((1)/(3)\pi t)+b_(3)sin(\pi t)+b_(5)sin((5)/(3)\pi t)+a_(7)sin((7)/(3)\pi t)
a_(1)cos((1)/(3)\pi t)+a_(3)cos(\pi t)+a_(5)cos((5)/(3)\pi t)+a_(7)cos((7)/(3)\pi t)
a_(0)+a_(1)cos((1)/(3)\pi t)+a_(2)cos((2)/(3)\pi t)+a_(3)cos(\pi t)+a_(4)cos((4)/(3)\pi t)
b_(1)sin((1)/(3)\pi t)+b_(2)sin((2)/(3)\pi t)+b_(3)sin(\pi t)+b_(4)sin((4)/(3)\pi t)(d) Which of the coefficients
a_(n)or
b_(n)are zero? For non-zero coefficients, round to 3 significant digits.
a_(n)=
b_(n)=