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tronxo
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Homework Statement
Using the complex representation of Fourier series, find the Fourier coefficients of the periodic function shown below. Hence, sketch the magnitude and phase spectra for the first five terms of the series, indicating clearly the spectral lines and their magnitudes
Homework Equations
Firstable, I don't know how indicate the spectral lines.
The other problem that i have is when i try to calculate the Cn coefficient and, therefore, the final serie. I don't know if it is right or not, and in case of it is right, I am not able to rewrite "my final function" into the correct answer, which i have it in one of my books.
The Attempt at a Solution
what i have done is:
Cn= 1/T∫(from 0 to T) f(t)*e^(-j*n*omega*t) dt
Cn=1/T ( ∫(from 0 to d) Vm*e^(-j*n*omega*t) dt + ∫(from d to T) 0 *e^(-j*n*omega*t) dt )
The second part of the integral is equal to 0, therefore:
Cn=1/T ∫(from 0 to d) Vm*e^(-j*n*omega*t) dt where omega= (2*pi/T)
Cn=1/T ∫(from 0 to d) Vm*e^(-j*n*(2*pi/T)*t) dt
Cn= Vm/T ∫(from 0 to d) e^(-j*n*(2*pi/T)*t) dt
Cn= Vm/(-j*n*(2*pi/T)*T) (limits of the resulting integral from 0 to d)[e^(-j*n*(2*pi/T)*t)]
Cn= Vm/ (-j*n*2*pi) [e^(-j*n*(2*pi/T)*d) - 1]
what is next?
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