  We analyse 3-min oscillations of microwave and EUV emission generated at
different heights of a sunspot atmosphere, studying the amplitude and frequency
modulation of the oscillations, and its relationship with the variation of the
spatial structure of the oscillations. High-resolution data obtained with the
Nobeyama Radioheliograph, TRACE and SDO/AIA are analysed with the use of the
Pixelised Wavelet Filtering and wavelet skeleton techniques. 3-min oscillations
in sunspots appear in the form of repetitive trains of the duration 8-20 min
(13 min in average). The typical interval between the trains is 30-50 min. The
oscillation trains are transient in frequency and power. We detected a
repetitive frequency drifts of 3-min oscillations during the development of
individual trains. Wavelet analysis shows three types of the frequency drift:
positive, negative and fluctuations without drift. The start and end of the
drifts coincide with the start time and end of the train. The comparative study
of 3-min oscillations in the sequences of microwave and EUV images show the
appearance of new sources of the oscillations in sunspots during the
development of the trains. These structures can be interpreted as waveguides
that channel upward propagating waves, responsible for 3-min oscillations. A
possible explanation of the observed properties is the operation of two
simultaneous factors: dispersive evolution of the upwardly-propagating wave
pulses and the non-uniformity of the distribution of the oscillation power over
the sunspot umbra with different wave sources corresponding to different
magnetic flux tubes with different physical conditions and line-of-sight
angles.
