e of extract the clock from the incoming data stream. This avoids the their spectral structure. Even if the received signal lacks a compo- need for a separate timing channel, as used in most computers for nent at the clock frequency, its spectral symmetry, which is inde- example, and makes it easier over the longer transmission distances pendent of sequence statistics can, after further processing, be used involved, to maintain the crucial phase relationship between the to provide a clock for retiming purposes. data and the clock at the point of decision making. Analysis (O'Reilly, 1984) reveals that any repetitive impulse Self-timing requires that the data signal is coded to ensure that sequence, including the important case where the sequence length there is either a clock component present in the transmitted signal tends to infinity, will possess a frequency spectrum with even or that such a component can be reliably extracted after processing amplitude symmetry and odd phase symmetry (that is, Hermitian at the receiver. The words reliably extracted imply that a satisfactory symmetry) about half the clock frequency. These symmetry condi- clock can be recovered which has a frequency, phase and amplitude tions, which are independent of sequence statistics, arise from the which is adequately immune from transmission distortions and periodic structure associated with the signal clock. interference, and from the effects of different data sequences. The Now, if a received sequence has little or no d.c. component, it latter requirement is found to be especially important in trans- follows directly from the above symmetry property that it will also mission systems containing a number of regenerative repeaters in have little or no f component. Most transmission codes, which tandem. Each repeater will experience some pattern dependent deliberately aim to suppress any d.c. content in a data sequence will variation or jitter on the phase of its extracted clock and this will be fall into this category. For such sequences f