distortionless transmission through a system
a signal is transmitted through a system without distortion, when all frequencies contained in the signal have the same delay. The frequency dependent delay is described by the group delay. If group delay is constant over frequency, all frequencies in the signal are delayed by the same amount.
Group delay on the other hand is the derivative of the phase response with respect to angular frequency. This derivative is only constant if the phase response is linear.
So this is the mathematical reason, why the phase response has to be linear for distortionless transmission.
1 members found this post helpful.