  Compressive sensing achieves effective dimensionality reduction of signals,
under a sparsity constraint, by means of a small number of random measurements
acquired through a sensing matrix. In a signal processing system, the problem
arises of processing the random projections directly, without first
reconstructing the signal. In this paper, we show that circulant sensing
matrices allow to perform a variety of classical signal processing tasks such
as filtering, interpolation, registration, transforms, and so forth, directly
in the compressed domain and in an exact fashion, \emph{i.e.}, without relying
on estimators as proposed in the existing literature. The advantage of the
techniques presented in this paper is to enable direct
measurement-to-measurement transformations, without the need of costly recovery
procedures.
