Time Domain Analysis and Synthesis of Notch Filters

In order to accurately measure noise levels in compandored communication systems, it is necessary to set the compandor characteristics at approximately the values associated with signal transmission. This is done by applying a so-called "holding tone" which is subsequently removed by a notch filter incorporated into the measuring set. This investigation originated in connection with the design of such a notch filter for an impulse noise counter. 1 The filter has to meet both frequency and time domain requirements. The frequency response requirements could be readily met with existing filter design procedures. However, the time domain characteristics of notch filters needed investigation with regard to the suitability for the present application. The time domain requirement is that the filter when combined with a C-message weighting filter 2 and excited with a stepped trigonometric time function at the notch frequency should, in the transient state, have only a specified overshoot level. This requirement is imposed by the necessity to distinguish in the measuring set between sudden gain and phase variations and impulse noise. To examine the transient response of notch filters, a class of such filters derived from low-pass filters by a frequency transformation is 283