I know the condition for two functions to be orthogonal. It is $\int_{a}^{b}f_1(x)f_2(x)dx=0$. Also, on YouTube and websites this kind of formula is used, no other.
I read from my book Signals and Systems by HSU 1st edition in solved example a slightly different definition. I would like some help to better understand the definition. It uses a complex number and some other extra items that perplex it,makes it more generic(?) and it gets me confused. What for all the extra stuff in the definition? Why not use a simple definition as in 1st paragraph?
Here it is:
$$\int_{a}^{b}f_m(x)f^*_k(x)dx = \begin{align}\begin{cases}a & m \neq k \\0 & m = k\end{cases} \end{align}$$
where $f^*_k(x)$ is a complex function. Also, $a \neq 0 $.