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# Sum Of Periodic Functions

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#### BlackOps

##### Full Member level 5
hi.

I have v(t) = cos 5t + 3sin (3t + Pi/4), how to find perioud of this function?

i know that perioud of first is 2Pi/5, second 2Pi/3, but how to find perioud of v(t)?

thanks.

#### flatulent

The constant phase shift in the second term does not affect the common period. Knowing that you should be able to find the answer. Then graph it to double check. One hint is to change the second term to a cos so that the constant phase shift is not there. A further hint is what value of t gives the same results as t=0?

#### BlackOps

##### Full Member level 5
actually i didnt understood ur further hint... well... usually value of 2Pi, doesnt affect value of expression...am i right?

and here.. as i saw, T1 = 2Pi/5 and T2 = 2Pi/3, so both have 2Pi in the upper line. so it means that perioud is 2Pi, right?

#### as_518

##### Member level 4
do you mean the frequeny of this function, the general solution for any function is to use fourier transform but since this function is already in the form of fourier transform

the fundmental frequency is 2Π/5 and the higher frequency is 5Π/3 the function has no common freqency or common period becuase it is multitone function.

#### BlackOps

##### Full Member level 5
what u mean as_518????? its just a simple problem, where i need to find perioud of the sum of two periodic functions.

answer is 2Pi, but i didnt get how it is done!

##### Full Member level 3
Yes, it's 2pi. It's the LCM(least common multiplier). For example, the period of 2 fn's with period 3 and 5 is 15. The first function is repeated every 3 unit, the other is every 5 unit. If you mark the beginning as in phase, the 2 functions will be in phase again at 15. Therefore, the addition of the 2 will be back at the starting point again every 15 unit.

### BlackOps

Points: 2

#### as_518

##### Member level 4
yes its 2pi -sorry for misunderstanding- one signal repeats itself 3 times ech 2pi the other repeats itself 5times ech 2pi so the addtion of the 2 signal will epeat it self ech 2pi. below is a plot of this function

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