Exponential Fourier Series

Thread Starter

GirishC

Joined Jan 23, 2009
58
Determine the Fourier series (one-sided) for the waveform in​
Fig. 3.7. Evaluate your result for
A ¼ 2, t ¼ 2 s, T ¼ 4 s.

My question is What slope do I need to take between 0 to T.

if I take t/T then I get wrong answer...could anybody tell me how to go about it?
 

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t_n_k

Joined Mar 6, 2009
5,455
I would take the slope as 1 between 0 and 2s and 0 between 2 & 4 sec.

So
x(t)=t for the interval t=0 to 2 seconds
and
x(t)=2 for the interval t=2 to 4 seconds
 

Thread Starter

GirishC

Joined Jan 23, 2009
58
With this I got the Cn as below. How do I further respolve and calculate the first seven harmonics?

I know I need to further evaluate it...but do not know how to proceed



 

t_n_k

Joined Mar 6, 2009
5,455
With this I got the Cn as below. How do I further respolve and calculate the first seven harmonics?

I know I need to further evaluate it...but do not know how to proceed



Would you mind re-posting your solution - I have a dead link.
 

Thread Starter

GirishC

Joined Jan 23, 2009
58
Here is the attachment. My apologies for improper update.

I am basically unable to understand how do I proceed in general to minimize the equation and eventually calculate the harmonics.
 

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t_n_k

Joined Mar 6, 2009
5,455
Assuming your general solution is correct you would make the substitutions for given values of T, \(\tau\) and A.

Then you would apply the Euler identities where applicable and evaluate each term for the required harmonic numbers n.
 
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