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We use high spatial and temporal resolution observations, simultaneouslyobtained with the New Vacuum Solar Telescope and Atmospheric Imaging Assembly(AIA) on board the Solar Dynamics Observatory, to investigate thehigh-frequency oscillations above a sunspot umbra. A novel time--frequencyanalysis method, namely the synchrosqueezing transform (SST), is employed torepresent their power spectra and to reconstruct the high-frequency signals atdifferent solar atmospheric layers. A validation study with synthetic signalsdemonstrates that SST is capable to resolving weak signals even when theirstrength is comparable with the high-frequency noise. The power spectra,obtained from both SST and the Fourier transform, of the entire umbral regionindicate that there are significant enhancements between 10 and 14 mHz (labeledas 12 mHz) at different atmospheric layers. Analyzing the spectrum of aphotospheric region far away from the umbra demonstrates that this 12~mHzcomponent exists only inside the umbra. The animation based on thereconstructed 12 mHz component in AIA 171 \AA\ illustrates that anintermittently propagating wave first emerges near the footpoints of coronalfan structures, and then propagates outward along the structures. Atime--distance diagram, coupled with a subsonic wave speed ($\sim$ 49 kms$^{-1}$), highlights the fact that these coronal perturbations are bestdescribed as upwardly propagating magnetoacoustic slow waves. Thus, we firstreveal the high-frequency oscillations with a period around one minute inimaging observations at different height above an umbra, and these oscillationsseem to be related to the umbral perturbations in the photosphere.

High-frequency Oscillations in the Atmosphere above a Sunspot Umbra