Using archival RXTE data we derive the 2-16 keV Fourier-resolved spectra of the Atoll source 4U 1728–34 in a sequence of its timing states as its low QPO frequency spans the range between 6 and 94 Hz . The increase in the QPO frequency accompanies a spectral transition of the source from its island to its banana states . The banana-states ’ Fourier-resolved spectra are well fitted by a single blackbody component with kT \sim 2 - 3 keV depending on the source position in the color – color diagram and the Fourier frequency , thus indicating that this spectral component is responsible for the source variability on these timescales . This result is in approximate agreement with similar behavior exhibited by the Z sources , suggesting that , as in that case , the bounday layer – the likely source of the thermal component – is supported by radiation pressure . Furthermore , it is found that the iron line at \sim 6.6 keV , clearly present in the averaged spectra , not apparent within the limitations of our measurements in the frequency-resolved spectra irrespective of the frequency range . This would indicate that this spectral component exhibits little variability on time scales comprising the interval 10 ^ { -2 } -10 ^ { 2 } seconds . In the island state the single blackbody model proved inadequate , particularly notable in our lowest frequency band ( 0.008 - 0.8 Hz ) . An absorbed powerlaw or an additive blackbody plus hard powerlaw model was required to obtain a satisfactory fit . Statisics do not allow unambiguous discrimination between these possible scenarios .