Averaging

The averaging of phase fluctutations will produce an amplitude decorrelation. For example, a phase jitter with gaussian noise $\phi$ will introduce a factor $e^{-\phi^2/2}$ of decorrelation if the real and imaginary parts are averaged (this is the classical definition of complex averages). CLIC offers the possibility to do averaging on the real and imaginary part or to average amplitude and phase (see SET AVERAGING for more details). In the latter case, the amplitude bias may lead to surprising results in the case of low signal-to-noise. For instance, the amplitude of the low spectral resolution windows may not be the same as the high spectral resolution spectral windows. Note also that if the averaging implies a decorrelation, then baseline based factors are introduced and the closure relationship does not hold anymore for amplitude.