Approximations by a mean or by running parabolae is properly valid, if
the signal has a parabolic shape. In real cases, the signal is more
complicated. To estimate systematic errors of the fitting curves from
the true ones, lets assume that the signal may be expanded into the
Taylor series:
where
Than the running fit may be written as
where coefficients
For symmetric fits s0=1, and s2k+1=0 for integer k. For even
m=2k,
