  Bandlimiting and timelimiting operators play a fundamental role in analyzing
bandlimited signals that are approximately timelimited (or vice versa). In this
paper, we consider a time-frequency (in the discrete Fourier transform (DFT)
domain) limiting operator whose eigenvectors are known as the periodic discrete
prolate spheroidal sequences (PDPSSs). We establish new nonasymptotic results
on the eigenvalue distribution of this operator. As a byproduct, we also
characterize the eigenvalue distribution of a set of submatrices of the DFT
matrix, which is of independent interest.
