A method for computing the power spectra of the in-phase and quadrature components of self-noise in a fourth-power clock recovery scheme is presented. This method is shown to be effective if the symbol waveform is time-limited or can be so approximated. The method applies to baseband signaling schemes such as pulse-amplitude modulation and to modulated carrier schemes such as quadrature-amplitude modulation. Comparison is made with the squaring-type recovery technique using cosine rolloff Nyquist pulses on the binary-phase-shift-keyed mode, at several excess bandwidth factors ( alpha ). It is shown that when alpha is less than 0.4, the fourth-power circuit gives less time jitter than the squarer for a noiseless channel. The method for self-noise spectrum calculation is verified by computer simulation. A prefilter that completely eliminates time jitter in the fourth-power clock recovery circuit is described.>

A method for obtaining power spectra for the self-noise components in phase and in quadrature to the desired generated clock signal for PAM systems is described. A previously recognized cross spectrum is also discussed. Results can be expressed either in a closed form or as the sum of rapidly convergent series, depending on the signalling waveform used. A computation of the in-phase and quadrature spectra for Nyquist pulses for excess bandwidth factors ranging from 0.1-0.9 is included, along with demonstration showing that for signalling waveforms with even or odd symmetry, cross power spectrum is zero at all frequencies. It is also shown that if the cross power spectrum is not zero due to asymmetry in the signalling waveform, sampling keyed to other than zero-crossing of the timing wave can give a lower timing jitter.>