Determining whether a sequence is periodic

[magnifik]

can someone help me determine whether this sequence is periodic?

[cos((2pi/3)n + pi/6) + 2sin((pi/4)n)] where n is all integers

i know that for a function to be periodic,
x(n) = x(n+N)

however, i am confused because both the cos and sin component contain n

please help. thx.

 

[VinnyCee]

cos\left(\frac{2\,\pi}{3}\,n\,+\,\frac{\pi}{6}\right)\,+\,sin\left(\frac{\pi}{4}\,n\right)

In general, in continuous time, the sum or product of two periodic signals is periodic, so your signal is periodic too.

 

[Dickfore]

Take N = 24 and see what happens.

 

[magnifik]

cos\left(\frac{2\,\pi}{3}\,n\,+\,\frac{\pi}{6}\right)\,+\,sin\left(\frac{\pi}{4}\,n\right)

In general, in continuous time, the sum or product of two periodic signals is periodic, so your signal is periodic too.

sorry, i forgot to specify that this is a discrete time signal. does that change anything?

 

[magnifik]

Take N = 24 and see what happens.

n + N = n + 24
x(n+N) = cos(2pi/3(n + 24) + pi/6) + sin(pi/4(n + 24))
= cos(2pi/3(n) + 16pi + pi/6) + sin(pi/4(n) + 6pi)
= cos(2pi/3(n) + pi/6) + sin(pi/4(n) + 6/pi)
so it's equal to x(n) because 2*k*pi doesn't change cos or sin
is this correct? thanks.

sorry for the ugly formatting

 

[Dickfore]

yes.

 

[magnifik]

yes.

thanks for the help. how did you get N = 24?