period of sum of signals

[Bhuvanesh123]

i am reading signals and system by oppenheim.There they shown way to found how to find period of a signal,but did not show to find the period of signal when it is in sum like x(t)= sin5t-4cos7t .Here i can find period of individual signal(i mean sin5t and cos7t) but with that how can find period of x(t).Thank you

 

[FvM]

I believe the answer can be directly related to finding the greatest common divisor. https://en.wikipedia.org/wiki/Common_divisor

In case of 5 and 7, it's 1

 

[Bhuvanesh123]

I believe the answer can be directly related to finding the greatest common divisor. https://en.wikipedia.org/wiki/Common_divisor

In case of 5 and 7, it's 1

in my solution book its given as LCM(2pi/5,2pi/7) is 2Pi as period .could you explain why is this

 

[ads-ee]

That solution says the resulting period is the Least Common Multiple (not a GCD) of the two periods of 2pi/5 and 2pi/7.

This basically means that if we pick a t then for some LCM of the periods of both signals there will be a time N*t that the signals will be the same as at t.

Using some simple counting as an example:

1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3       123 repeated (period of 3)
1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5   12345 repeated (period of 5)  
S                             R

One result (which may not be the smallest) will be multiplying the periods of each to find the period of the combined, i.e 3*5 = 15

 

[FvM]

Yes, it's least common multiple when you ask for period. It's also GCD in frequency.

 

[ads-ee]

Yes, it's least common multiple when you ask for period. It's also GCD in frequency.

Ah, yes:idea:. We were looking at things from the opposite sides of the "coin".