  This paper discusses sample allocation problem (SAP) in frequency-domain
Compressive Sampling (CS) of time-domain signals. An analysis that is relied on
two fundamental CS principles; the Uniform Random Sampling (URS) and the
Uncertainty Principle (UP), is presented. We show that CS on a single- and
multi-band signals performs better if the URS is done only within the band and
suppress the out-band parts, compared to ordinary URS that ignore the band
limits. It means that sampling should only be done at the signal support, while
the non-support should be masked and suppressed in the reconstruction process.
We also show that for an N-length discrete time signal with K-number of
frequency components (Fourier coefficients), given the knowledge of the
spectrum, URS leads to exact sampling on the location of the K-spectral peaks.
These results are used to formulate a sampling scheme when the boundaries of
the bands are not sharply distinguishable, such as in a triangular- or a
stacked-band- spectral signals. When analyzing these cases, CS will face a
paradox; in which narrowing the band leads to a more number of required
samples, whereas widening it leads to lessen the number. Accordingly; instead
of signal analysis by dividing the signal's spectrum vertically into bands of
frequencies, slicing horizontally magnitude-wise yields less number of required
sample and better reconstruction results. Moreover, it enables sample reuse
that reduces the sample number even further. The horizontal slicing and sample
reuse methods imply non-uniform random sampling, where larger-magnitude part of
the spectrum should be allocated more sample than the lower ones.
