2 research outputs found
Time-frequency analysis of signals using support adaptive Hermite-Gaussian expansions
Cataloged from PDF version of article.Since Hermite–Gaussian (HG) functions provide an orthonormal basis with the most compact time–
frequency supports (TFSs), they are ideally suited for time–frequency component analysis of finite energy
signals. For a signal component whose TFS tightly fits into a circular region around the origin, HG
function expansion provides optimal representation by using the fewest number of basis functions.
However, for signal components whose TFS has a non-circular shape away from the origin, straight
forward expansions require excessively large number of HGs resulting to noise fitting. Furthermore, for
closely spaced signal components with non-circular TFSs, direct application of HG expansion cannot
provide reliable estimates to the individual signal components. To alleviate these problems, by using
expectation maximization (EM) iterations, we propose a fully automated pre-processing technique which
identifies and transforms TFSs of individual signal components to circular regions centered around the
origin so that reliable signal estimates for the signal components can be obtained. The HG expansion
order for each signal component is determined by using a robust estimation technique. Then, the
estimated components are post-processed to transform their TFSs back to their original positions.
The proposed technique can be used to analyze signals with overlapping components as long as the
overlapped supports of the components have an area smaller than the effective support of a Gaussian
atom which has the smallest time-bandwidth product. It is shown that if the area of the overlap
region is larger than this threshold, the components cannot be uniquely identified. Obtained results on
the synthetic and real signals demonstrate the effectiveness for the proposed time–frequency analysis
technique under severe noise cases.
© 2012 Elsevier Inc. All rights reserved