Jitter Comparison of Tones Generated by Squaring and by Fourth-Power Circuits

Successful detection of the symbols in a pulse-modulated waveform requires a knowledge of the pulse repetition period T. Specifically, if the signal s(t) is of the form s(t) = E n=-- = ang(t-nT) (1) where an are independent equiprobable binary symbols having values ±1, knowledge of T is required for proper sampling of s(t) to recover the an. Due to small differences in transmitter and receiver oscillators, a priori information concerning T is not usually sufficient, and constant updating of the precise current value of T is required. Often one prefers to deduce such information directly from eq. (1), rather than directly transmitting a tone at frequency 1 IT Hz. A very popular method is to pass s(t) through an appropriate nonlinear circuit (e.g., a square-law) so that a tone is generated at frequency 1 IT.1 For example, using the square-law operation we have the following identity: s2(t)= --oo (iang(t-nT))2= / n =--co t gHt-nT) n,m + ny^m £ anamg(t-nT)g(t-mT) (2)