  A specific type of artifacts, that originate due to displacement of the image
of a moving object along the digital (pixel) matrix of receiver are analyzed in
detail. The criteria of appearance and the influence of these artifacts on the
study of long-term oscillations of sunspots are deduced. The obtained criteria
suggest us methods for reduction or even elimination of these artifacts. It is
shown that the use of integral parameters can be very effective against the
artifact distortions. The simultaneous observations of sunspot magnetic field
and ultraviolet intensity of the umbra have given the same periods for the
long-term oscillations. In this way the real physical nature of the oscillatory
process, which is independent of the artifacts have been confirmed again. A
number of examples considered here confirm the dependence between the periods
of main mode of the sunspot magnetic field long-term oscillations and its
strength. The dependence was derived earlier from both the observations and the
theoretical model of the shallow sunspot. The anti-phase behavior of time
variations of sunspot umbra area and magnetic field of the sunspot demonstrates
that the umbra of sunspot moves in long-term oscillations as a whole: all its
points oscillate with the same phase.
