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Fourier Series Oppenheim

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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.
 

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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.
 

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..

unfortunately i don't have the book at this time but i guess i know the example you are talking about.

i think you are talking about the example of square wave which they (oppenheim,willsky and nawab) used in the theory and and most of the problems as well.

T1 in that example i think was the time during which the pulse remains high and it was expressed as a fraction of T(the period of waveform). then they have simulated the waveform for different values of T1 which is waveform with different duty cycles.

then please explain this
I dont understand that what effect will it have on original signal as T is only the period of the signal
Click to expand...
are you talking about the effect of changes in T on fourier series?

if so ,then increase in T will contract stems of fourier series and decrese would have opposite effect.

Actually in that example they tried to show that the number and magnitude of stems(frequecy components and their weight) depends upon the duty cycle.

sorry if i failed to answer your question probably bcoz i don't have the book right now or may be bcoz you hav'nt

i just looked at your 2nd post

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.
Click to expand...

actually in that example they have defined T1 in terms of T like T1=T/4 i guess. as long as you define T1 in terms of T ,changing T would have direct effect on T1 i mean if T increases , T1 does the same and vice versa .and their fourier effect i have explaind above.
But if you define T1 as absolute numbers independent of T like T1=2ms whatever the T is. then changing T would have no effect on width of pulse but it does has an effect on duty cycle. i you don't know about duty cycle it is ratio of on time of waveform to the total period. so if T1 is absolute , and T increases then duty cycle also increases. but in the case if T1 is not absolute , Duty cycle remains fixed but the pulse width increases.

Best of Luck. reply if you don't understand

Regards
Ejaz Ahmed
Click to expand...
 

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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