Why sin(0.2*x + pi) is aperiodic function?

Question

I know this might be too easy to be a question... but I can't get why sin(0.2*x + pi) is aperiodic?..

I tried to plot this in matlab and that's what I got:

Matlab sin wave

That should be periodic right? Instead in "Schaum's Outline of Digital Signal Processing" book it says it's aperiodic

Solution of Schaum's Outline book

http://math.stackexchange.com/ – user2244984 Apr 20 '13 at 12:01 — user2244984, Apr 20 '13 at 12:01

score 3 · Accepted Answer · answered Apr 20 '13 at 12:03

3

The function f(x) = sin(pi + 0.2*x) is periodic.

The sequence sin(pi + 0.2*n) where n=0, 1, ... is not periodic.

answered Apr 20 '13 at 12:03

6502

it should be _discrete_ if I understand this correctly. – user2244984 Apr 20 '13 at 12:05
That's true it's discrete. Now i get it :) thanks – Kareem Mohamed Apr 20 '13 at 12:54

score 2 · Answer 2 · answered Apr 20 '13 at 12:09

sin(0.2*x + pi), x in R (i.e. x - real) is periodic, as we could find such x0 that sin(0.2*x + pi) = sin(0.2*(x + x0) + pi)

sin(0.2*x + pi), x in N_0 (i.e. x - natural and zero) is not periodic. You've provided exactly the proof of that fact in page screenshot.

2 Answers2