Jitter probability in the breakpoints of discrete sparse piecewise-constant signals

It is shown that jitter is fundamentally inherent to the break-points of discrete sparse piecewise-constant signals measured in noise. No one estimator, even ideal, is able to provide the jitter-free breakpoints detection with unit probability. Even so, the jitter distribution in such signals was unknown so far. We have shown that for noise having white properties the jitter can be approximated with the discrete skew Laplace distribution irrespective of the segmental distributions. The theory was tested in Gaussian and heavy-tailed Cauchy noise environments and good correspondence was demonstrated.