#### Question 4.1

## Group delay – filters

#### Group delay is defined as the rate of change of phase shift with frequency. For a filter with a linear phase response, the rate of change of phase with frequency is constant and hence the group delay will be a fixed, though non-zero, value over all frequencies, that is, a pure time delay. For a non-linear phase response, the group delay will vary with frequency as shown here, with the effect that data pulses or symbols passing through the filter are smeared by the different delays across the frequency components, reintroducing ISI into the signal. Both gain and phase/group delay distortion can be compensated to some extent with the use of equalization circuits, which in practice are themselves digital filters which are configured to compensate for the imperfections of the usually analogue filters within the system, or imperfections in the channel itself. |