Evalution of the Effects of Notch Filters on Digital Data Transmission

The performance impairment resulting from the insertion of a narrow-band rejection filter (notch filter) in a data transmission channel is evaluated. To isolate the effects of notch filtering, it is assumed that, before inserting the notch filter, the data signal is an idealized pulse amplitude modulation (PAM) signal using a pulse shape which produces no intersymbol interference (Nyquist pulse). The intersymbol interference resulting from the notch is examined in terms of 1) its maximum value and 2) its mean-squared value. It is shown that the maximum interference criterion is inappropriate; since it will always exceed the signal pulse amplitude regardless of the shape or rejection bandwidth of the notch filter (a notch always closes the binary eye pattern). The mean-squared interference is easily evaluated in terms of the notch characteristic, and furthermore, this quantity leads to a simple means for predicting the tolerable notch bandwidth for maintaining a specified error performance with additive Gaussian noise. The mean-squared interference for some simple notch filter realizations is presented.