A Conjugate-Gradients Based Method
for Harmonic Retrieval Problems that
Does Not Use Explicit Signal Subspace Computation
F. S. V. Bazan, Ph. L. Toint and M. C. Zambaldi
Report 97-16
The harmonic retrieval problem consists of estimating frequencies and decay
factors of multiple exponential signals from experimental measurements. At
variance with most available algorithms, which are based on the singular
value decomposition (SVD) and the explicit identification of the so-called
``signal subspace'', we present an alternative method in which this
explicit identification is not needed. We propose to replace it by an {\em
implicit} estimation using the concept of predictor matrices and
algorithmically realized using conjugate gradients. We finally discuss some
numerical examples, both synthetic and from a real application, showing
that the new method produces results of an accuracy comparable to that of
SVD-based subspace techniques, but without requiring a priori knowledge of
the dimension of the signal subspace and at a lower computational cost.