Periodicity of a constant signal! This can be a very silly question, but I'm quite confused:


If we take the Fourier transform of any constant signal, we get an impulse at zero, which says that its frequency is zero and, hence, it is non-repeating and its period is infinity.
By the definition of a periodic signal, $$F(z+p) = F(z)$$ therefore, for a constant function $$F(z) = c$$ $$F(z+p) = c, \forall p &gt;0$$ Therefore, a constant function is periodic, but its period is undefined or can be defined as anything.


Which of the above arguments are correct and why? Please clarify. Thanks in advance.
As you say, the constant function is periodic. A signal $x(t)$ is said to be periodic with period $p$ or to have a period $p$ if there exists a $p&gt;0$ such that $x(t+p)=x(t)$ for all real numbers $t$. Note that I said "a period" instead of "the period" -- periodic signals have an infinite number of periods, maybe even an uncountable infinite of them!

Often, what is referred to as the period of a signal is actually more formally described as the "fundamental period", which is the smallest among all periods.

So, a constant signal is periodic, it has an uncountably infinite number of periods (since any real number $p&gt;0$ is a period), but it does not have a fundamental period.