0

I'm trying to understand the fourier series coefficients for trig fourier series, and I came across the general expansion written in this form.

Fourier series general

And their respective formulas, and I found an inconsistency in stuff online and what is taught by my professor. My prof gives the formula for a0 with the coefficient 2/T0 in the context for writing the series for a square wave, T0 being the fundamental frequency through a derivation with integration A0 equation 1

However, I found another formula for the same term online, which consists of something really similar but slightly different. a0 function 2

Which one is correct (maybe both are correct?) and what is the significance of the 2/T0 or 1/T0 term in front? I am interpreting the 1/T0 as sort of an average value for across a period which kind of makes sense, but what about the 2/T0, why does that make sense? When should I be using each coefficient?

Wolfking
  • 101
  • It does somewhat clarifies some things, does it mean that both formulas are correct and they differ because of their definitions, perhaps in my profs lectures, they are defined as somewhat of a0/2 just for convenience for the general formula of ak? – Wolfking Feb 07 '24 at 06:31
  • 2
    Yes, they are just different conventions. Absent the convention, "$a_0$" means nothing. If you value a consistent formula for $a_k$, then you need the Fourier series for $f$ to have $a_0/2$. If you value the constant in the series being $a_0$ as the coefficient of an invisible "$\cos(0\omega_0t)$", then you need a separately defined formula for $a_0$. – Brian Moehring Feb 07 '24 at 06:32

0 Answers0