  We present a procedure that adds a number of desirable features to standard
exponential analysis algorithms, among which output reliability, a
divide-and-conquer approach, the automatic detection of the exponential model
order, robustness against some outliers, and the possibility to parallelize the
analysis. The key enabler for these features is the introduction of uniform
sub-Nyquist sampling through decimation of the dense signal data. We actually
make use of possible aliasing effects to recondition the problem statement
rather than that we avoid aliasing.
  In Section 2 the standard exponential analysis is described, including a
sensitivity analysis. In Section 3 the ingredients for the new approach are
collected, of which good use is made in Section 4 where we essentially bring
everything together in what we call VEXPA.
  Some numerical examples of the new procedure illustrate in Section 5 that the
additional features are indeed realized and that VEXPA is a valuable add-on to
any stand-alone exponential analysis. While returning a lot of additional
output, it maintains a favourable comparison to the CRLB of the underlying
method, for which we here choose a matrix pencil method. Moreover, the output
reliability of VEXPA is similar to that of atomic norm minimization, whereas
its computational complexity is far less.

Numerical Analysis;Numerical Analysis