  This paper presents a unified framework to tackle estimation problems in
Digital Signal Processing (DSP) using Support Vector Machines (SVMs). The use
of SVMs in estimation problems has been traditionally limited to its mere use
as a black-box model. Noting such limitations in the literature, we take
advantage of several properties of Mercer's kernels and functional analysis to
develop a family of SVM methods for estimation in DSP. Three types of signal
model equations are analyzed. First, when a specific time-signal structure is
assumed to model the underlying system that generated the data, the linear
signal model (so called Primal Signal Model formulation) is first stated and
analyzed. Then, non-linear versions of the signal structure can be readily
developed by following two different approaches. On the one hand, the signal
model equation is written in reproducing kernel Hilbert spaces (RKHS) using the
well-known RKHS Signal Model formulation, and Mercer's kernels are readily used
in SVM non-linear algorithms. On the other hand, in the alternative and not so
common Dual Signal Model formulation, a signal expansion is made by using an
auxiliary signal model equation given by a non-linear regression of each time
instant in the observed time series. These building blocks can be used to
generate different novel SVM-based methods for problems of signal estimation,
and we deal with several of the most important ones in DSP. We illustrate the
usefulness of this methodology by defining SVM algorithms for linear and
non-linear system identification, spectral analysis, nonuniform interpolation,
sparse deconvolution, and array processing. The performance of the developed
SVM methods is compared to standard approaches in all these settings. The
experimental results illustrate the generality, simplicity, and capabilities of
the proposed SVM framework for DSP.
