Theoretical and numerical aspects of an SVD-based method for band-limiting finite-extent sequences

摘要

The authors present an SVD-based method for band-limiting over-sampled discrete-time finite-extent sequences. For this purpose, they show that finite-extent band limitation is best defined in terms of the discrete prolate spheroidal sequences rather than complex exponentials. Their method has maximum energy concentration as defined in the paper, its dimension agrees asymptotically with Slepian's (1978) dimension result, and the method specializes correctly to the discrete-time Fourier transform as the sample size tends to infinity. They propose an efficient computational method, based on the Lanczos algorithm, for computing only the necessary singular vectors. The SVD is signal-independent, only needs to be done once and can be precomputed. The SVD-based band limitation itself is not necessarily much slower than the fast Fourier transform for sample sizes on the order of 4096.