Time domain analysis and synthesis of notch filters

The response of notch filters to sudden excitations is analyzed. Unit step and stepped trigonometric inputs are considered for the class of filters derived from low-pass networks by a frequency transformation. It is possible in some cases to approximate the transient solutions in terms of Laguerre functions and deduce general properties of notch filters from these solutions. The use of phasing sections to modify the transient response is also examined. It is shown that this method can be used to effectively reduce the overshoot in the response to a stepped trigonometric excitation.