THEORETICAL AND NUMERICAL ASPECTS OF AN SVD-BASED METHOD FOR BAND-LIMITING FINITE-EXTENT SEQUENCES

We present an SVD-based method for band-limiting over-sampled discrete -time finite-extent sequences. For this purpose, we show that finite-e xtent band limitation is best defined in terms of the discrete prolate spheroidal sequences rather than complex exponentials. Our method has maximum energy concentration as defined in the paper, its dimension a grees asymptotically with Slepian's dimension result, and the method s pecializes correctly to the discrete-time Fourier transform as the sam ple size tends to infinity. We propose an efficient computational meth od, based on the Lanczos algorithm, for computing only the necessary s ingular vectors. The SVD is signal-independent, only needs to be done once and can be precomputed. The SVD-based band limitation itself is n ot necessarily much slower than the fast Fourier transform for sample sizes on the order of 4096.