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.
문제
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:
That should be periodic right? Instead in "Schaum's Outline of Digital Signal Processing" book it says it's aperiodic
해결책
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.
다른 팁
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.