By Topic

Adapted and Adaptive Linear Time-Frequency Representations: A Synthesis Point of View

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$33 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

4 Author(s)
Peter Balazs ; Acoustics Research Institute, Academy of Science, Wien, 1040, Austria ; Monika Doerfler ; Matthieu Kowalski ; Bruno Torresani

A large variety of techniques exist to display the time and frequency content of a given signal. In this article, we give an overview of linear time-frequency representations, focusing mainly on two fundamental aspects. The first is the introduction of flexibility, more precisely, the construction of time-frequency waveform systems that can be adapted to specific signals or specific signal processing problems. To do this, we base the constructions on frame theory, which allows many options while still ensuring perfect reconstruction. The second aspect is the choice of the synthesis framework rather than the usual analysis framework. Instead of considering the correlation, i.e. the inner product, of the signal with the chosen waveforms, we find appropriate coefficients in a linear combination of those waveforms to synthesize the given signal. We show how this point of view allows the easy introduction of prior information into the representation. We give an overview of methods for transform domain modeling, in particular those based on sparsity and structured sparsity. Finally, we present an illustrative application for these concepts: a denoising scheme.

Published in:

IEEE Signal Processing Magazine  (Volume:30 ,  Issue: 6 )