Abreu, L. D., Romero, J. L. (2017): MSE estimates for multitaper spectral estimation and off-grid compressive sensing, in: IEEE Transactions on Information Theory 63/12, 7770-7776. (article)


    We obtain estimates for the Mean Squared Error (MSE) for the multitaper spectral estimator and certain compressive acquisition methods for multi-band signals.We confirm a fact discovered by Thomson [Spectrum estimation and harmonic analysis, Proc. IEEE, 1982]: assuming bandwidth W and N time domain observations, the average of the square of the first K = [2NW] Slepian functions approaches, as K grows, an ideal band-pass kernel for the interval [-W,W]. We provide an analytic proof of this fact and measure the corresponding rate of convergence in the L1 norm. This validates a heuristic approximation used to control the MSE of the multitaper estimator. The estimates have also consequences for the method of compressive acquisition of multi-band signals introduced by Davenport and Wakin, giving MSE approximation bounds for the dictionary formed by modulation of the critical number of prolates.