Prove the sum of 2 signals is periodic?

[LM741]

hey guys - just a question regarding a systems and signals course:

if I've got two disctrete signals: x1[n] and x2[n]

if i know both signals are periodic (individually) how do i prove the sum of these signals is periodic?

requirement for periodicty (one signal): x[n+N] = x[n]

where n and N are integers - remeber - discrete signals!

thanks!

John

 

[EvLer]

Lcm (n1,n2)

 

[LM741]

EvLer >> Please elaborate...lowest common multiple of n1 and n2? not entirely sure what you mean ..thanks...

 

[Mohammad]

let k = lcm(n1, n2) which is the lowest common multiplier

x(n+k) = x1(n+k) + x2(n+k)

Since k is the lowest common multiplier, that means that it will satisfy the requirement for both signals (for example: x1(n+2) = x1(n+4) = x1(n+6) = ... ). So you have

x(n+k) = x1(n) + x2(n)

 

[LM741]

Thanks Mohammad!

John