Fourier Series Oppenheim

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urwelcome

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In the book of Oppenheim on Signals and Systems in chapter No 3 and example No.3.5 the Fourier series for a pulse is shown for different T and fixed T1 ...I dont understand that what effect will it have on original signal as T is only the period of the signal and if this is so than how can we increase or decrease the period because signal is same with same period..

Please some body explain it ,,,,

Best Regards to all Fourier lovers ...
 

Ok, I located the example problem. Frankly, I dont understand your question. Are you speaking about Figure 3.7?

The figure explains the effect of different fundamental period T of the rectangular pulse. If T = 4T1, meaning, the rectangle pulse lying in the origin extents from -2T1 to 2T1 and if T = 8T1, then same lies between -4T1 to 4T1.

In these two cases, the fundamental period changes, for same T1. T is a function of T1. In the example they have tried to show how the fourier series coefficients change as the period T of the rectangular waveform changes.

Does this clarify your doubt?

cedance.
 

    urwelcome

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Dear I want to ask that by changing the value of T i,e its period and keeping T1 constant what happens to the width of the pulse which is origionally from -T1 to T1 i,e 2T1...

Thank you for ur help.
 

 

Hi, The width of the pulse is the same. As I told before, the function is piecewise defined. So, from -T1 to T1, the magnitude of the rect pulse is 1 and 0 in the other interval range (-T/2 to -T1 and T1 to T/2).

However, you get the coefficients different coz, in order to reconstruct the pulse with period say, -2T1 to 2T1 as in the case T = 4T1, and say for the pulse -4T1 to 4T1, as in the case T = 8T1, the period of the pulse is changed. Meaning, the pulse repeats itself after certain duration.

Consider a sine way with a period of 2 Hz or cycles/sec. In this case, the pulse repeats after every 0.5 second. Now if the fundamental period of the sinusoid is changed, the the fourier coefficients will be changed accordingly (in this case its only 1 frequency, may sound absurd), in order to summate and get back the same signal with same freqeuncy

hope the reply was convincing.

regards,
cedance.
 

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