  In this paper we introduce two new algorithms for stable approximation with
and recovery of short cosine sums. The used signal model contains cosine terms
with arbitrary real positive frequency parameters and therefore strongly
generalizes usual Fourier sums. The proposed methods both employ a set of
equidistant signal values as input data. The ESPRIT method for cosine sums is a
Prony-like method and applies matrix pencils of Toeplitz+Hankel matrices while
the ESPIRA method is based on rational approximation of DCT data and can be
understood as a matrix pencil method for special Loewner matrices. Compared to
known numerical methods for recovery of exponential sums, the design of the
considered new algorithms directly exploits the special real structure of the
signal model and therefore usually provides real parameter estimates for noisy
input data, while the known general recovery algorithms for complex exponential
sums tend to yield complex parameters in this case.
