The effect upon pulse response of delay variation at low and middle frequencies

Calculations are given for the magnitude and form of the distortion introduced into a square wave by a network or system which exhibits uniform transmission except for increasing (or decreasing) phase delay in the low-mid-frequency region. The fractional peak distortion is found to be equal to twice the area under the curve relating Tn to frequency, where Tn is the delay relative to that at high frequencies. The waveform of the distortion is given for several simple shapes of curve for Tn. This distortion is especially characteristic of vestigial-sideband systems, and occurs in television as a `pre-shoot¿ before a transition and as a smear (in principle equal, but opposite, to the pre-shoot) after it.