Editing Self-clocking signal (section)

== Analog examples ==
[[Amplitude modulation]] – [[modulation|modulating]] a signal <math>M(t)</math> by changing the amplitude of a carrier wave, as in:
:<math>y(t) = M(t) \cdot \cos(\omega_c t),</math>
is self-clocking, as the zero crossings serve as a [[clock pulse]].

One may consider this clock pulse redundant information, or at least a wasteful use of channel capacity, and duplex the channel by varying the phase, as in [[polar modulation]], or adding another signal that is 90° out of phase (a sine wave), as in [[quadrature modulation]]. The result is to send twice as many signals over the channel, at the cost of losing the clock, and thus suffering signal degradation in case of [[clock drift]] (the analog equivalent of bit drift).

This demonstrates how encoding clocking or synchronization in a code costs channel capacity, and illustrates the trade-off.