B.S.T.J. Briefs: Application of Automatic Transversal Filters to the Problem of Echo Suppression

Equation (6) is easily solved to give p(k) =p(0)[l + K t r 2 ( H ) ] . (8) Then JjmpC*)-p0)[l + j ^ ] . (9) T h e bracketed term in (8) or (9) gives the enhancement of error probability due to errors made on all previous pulses. To compare results obtained by application of (9) with those obtained experimentally by R. D. Howson, 2 we take b = g 0 = exp ( -- a n d 7i = --£7o(l -- exp ( -- j ) ) . Over a wide range of S / N ratios of interest, analysis based upon (9) predicts about a 0.6-dB S / N penalty of this system over the ideal case of no low frequency cutoff. Agreement with experiment is excellent. It should be noted t h a t the enhancement term in (9) is very close to unity and the S / N penalty is due essentially to the reduction of the pulse peak by the low-frequency cut-off. In a future paper we will show (i) how Zador's approach can be extended to a wider class of systems, and Hi) how the approximation given herein can be used and improved when necessary, to arrive at meaningful quantitative results. REFERENCES 1. Zador, P. L., Error Probabilities in Data System Pulse Regenerator with DC Restoration, B.S.T.J., 45, July, 1966, pp. 979-984. 2. Flavin, M. A., Gerrish, A. M., Howson, R. D., and Salz, J., unpublished work.