I keep reading that a constant group delay over a frequency band is desirable for a filter. But a constant group delay means a linear decrease in the phase delay, which would distort the signal.
Let's assume that I have a group delay of 5 [time units] over a frequency band from 100 Hz to 110 Hz. That means that the phase delay is $-5\omega + c$.
- the 100 Hz component will be delayed by 500 + c rad
- the 101 Hz component will be delayed by 505 + c rad
- the 102 Hz component will be delayed by 510 + c rad
Considering that different frequencies components have different phase delays, the signal will be distorted.
So why is a flat group delay response desirable for a filter?