How can understand periodicity of a Signal from frequency domain representation?
A signal is periodic if and only if its frequency spectrum is


discrete (contains only pulses covering a single locus with a finite
area).
all of those discrete pulses occur at an integral multiple of one
frequency (the periodicity).


If you have, for example, $\cos(\pi t)+ \cos(t)$, the resulting spectrum is discrete but the function is not periodic.