0

In mathematics, we learned that a constant function is periodic but does not have a smallest positive period (fundamental period). Consequently, I conclude that a constant signal has no frequency. However, in physics, we learn that a constant signal is a sinusoid with a frequency of zero. I don't understand because if the frequency were zero, then by definition $f=\frac 1 T$, the fundamental period would be infinite.

What am I missing exactly?

Ziad
  • 37
  • 2
    That usage by physicists is not universal, and it is sloppy in my opinion. – coffeemath Oct 18 '23 at 10:38
  • 5
    It is not uncommon to have varying conventions for edge cases even within mathematics. – Klaus Oct 18 '23 at 10:38
  • You could go for something like $$ T=\inf {t>0 \mid f(x+t)=f(x) ; \forall x \in \mathbb{R} } $$ as the definition for smallest period. But like other people said, its not universally defined. – F. Conrad Oct 18 '23 at 10:40
  • Do you know of a consensus between mathematicians and physicists on the concept of period or fundamental period? – Ziad Oct 18 '23 at 10:46
  • I asked this question to a physics professor, and he provided me with this consensus. For a physicist, frequency is the number of oscillations in 1 second. So, a mathematical definition could be as follows: For a constant signal that does not oscillate, conventionally, its frequency is considered to be zero. For a non-constant signal that has a fundamental period T, we define the frequency as f=1/T – Ziad Oct 18 '23 at 16:18

0 Answers0