Linear phase filters delay all frequencies by the same amount. Why aren't they called Constant phase filters instead of Linear phase?
As I understand, if there is an input signal with two components $f_1$ and $f_2$, and it is passed through a linear phase system which introduces a delay $t$, $f_1$ is delayed by $t$, and $f_2$ is also delayed by $t$.
To what property does the phase have a linear relationship with? Could someone provide some insight into this? Some Math would be helpful.