Exact trigonometric superfast inverse covariance representations

Abstract

This paper shows that superfast inverse covariance representations are not limited to DFT based formulas, and can be obtained similarly for trigonometric transforms, such as discrete cosine and discrete sine matrices. Unlike commonly implied by some authors, the use of real transforms does not depend on any symmetry condition in the columns of the corresponding data matrix. This result follows the state-of-the-art of the displacement approach to matrices in connection to recurrence polynomial realizations, where the choice of Chebyshev bases leads to DCT/DST decompositions, directly applicable to block frequency-domain equalization using real data.