is x(n)=cos(8/15*Pi*n) a periodic function?

Question

hartnn · Answer

$\cos (2\pi n/T+\phi)$ is periodic with period = T
so, here, compare 8/15*Pi  with 2 pi /T and get T

anonymous · Answer

so irrespective all cosine and sine funcions are periodic?

hartnn · Answer

nopes, its like , to find whether the signal is periodic, plug in n by 'n+p' (i'll use 1/T = f )
$x(n+p)=\cos (2\pi fn) = \cos(2\pi fn+2\pi fp)=x(n)$ 
for this, 
its required that 2pi f p = 2pi f n 
so, f = m/p and this f must be rational for the signal to be periodic

anonymous · Answer

oh cool, thanks a lot got it :) :)

hartnn · Answer

welcome ^_^
bdw, what u got? periodic or a-periodic ? just to verify...

anonymous · Answer

i equated 8/15*Pi=2*Pi/T which gave me T=15/4, so i guess its a-periodic

hartnn · Answer

but 15/4 is rational. and rational means the signal is periodic..

hartnn · Answer

f= 4/15 = rational

anonymous · Answer

yup sorry periodic T=15/4 is what i meant, since like you explained its rational :)

hartnn · Answer

ok :)

anonymous · Answer

can i bother you with one last question?

hartnn · Answer

sure!

anonymous · Answer

Thanks :) what if its a sum of two functions like for example x(t)=cos2t+sin3t ?

hartnn · Answer

ok, sorry for late reply, 
find the individual period and then period of overall signal will be LCM of those 2 periods.

anonymous · Answer

oh cool thanks again :) :)