I and Q decomposition of self-noise in square-law clock regenerators

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