Fast reconstruction of nonuniformly sampled bandlimited signal using Slepian functions

In this paper, we present an algorithm for fast reconstruction of bandlimited signal from nonuniform samples using shift-invariant space with Slepian function as a generator. The motivation to use Slepian functions is that they are bandlimited and most of their energy is concentrated in the finite time interval [-τ, τ]. This allows their truncation in time with controllable error, and results in a reduction of computational complexity of reconstruction process to O(N L²). where N is number of samples, and L ≈ τ. As decreasing τ increases the truncation error, the algorithm offers a tradeoff between speed and accuracy. The simulation example of signal reconstruction is provided.