  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 boundary 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. Statistics do not allow unambiguous
discrimination between these possible scenarios.
