Hello everyone i would like to find if a sum of periodic systems is periodic, and if it is i would like to find its fundamental period.
When i have two signals i think i am capable of doing it
lets assume that the period of the first signal is T1=2/3
and the period of the second is T2=3/4
T1/T2=8/9 which is rational so the sum of these two periodic signals is periodic too
for its fundamental period i do T12=T1*k=T2*d
=>k/d=T2/T1=9/8
=>k=9 and d=8 so T12=6
But what happens when you have the sum of three periodic signals with three periods T1,T2,T3 ?
I tried making first the sum of the two signals and then again with the third but the period i was finally doing wasnt the same for every combination, can you help me ?
I actually have made some miscalculations, i find the same result no matter the combination
But is this way right or is there any other way ?
thanks in advance
When i have two signals i think i am capable of doing it
lets assume that the period of the first signal is T1=2/3
and the period of the second is T2=3/4
T1/T2=8/9 which is rational so the sum of these two periodic signals is periodic too
for its fundamental period i do T12=T1*k=T2*d
=>k/d=T2/T1=9/8
=>k=9 and d=8 so T12=6
But what happens when you have the sum of three periodic signals with three periods T1,T2,T3 ?
I tried making first the sum of the two signals and then again with the third but the period i was finally doing wasnt the same for every combination, can you help me ?
I actually have made some miscalculations, i find the same result no matter the combination
But is this way right or is there any other way ?
thanks in advance
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