# An Analysis of Minimum Entropy Time-Frequency Distributions

Abstract (Summary)

The subject area of time-frequency analysis is concerned with creating meaningful representations of signals in the time-frequency domain that exhibit certain properties. Different applications require different characteristics in the representation. Some of the properties that are often desired include satisfying the time and frequency marginals, positivity, high localization, and strong finite support. Proper time-frequency distributions, which are defined as distributions that are manifestly positive and satisfy both the time and frequency marginals, are of particular interest since they can be viewed as a joint time-frequency density function and ensure strong finite support. Since an infinite number of proper time-frequency distributions exist, it is often necessary to impose additional constraints on the distribution in order to create a meaningful representation of the signal. A significant amount of research has been spent attempting to find constraints that produce meaningful representations.
Recently, the idea was proposed of using the concept of minimum entropy to create time-frequency distributions that are highly localized and contain a large number of zero-points. The proposed method starts with an initial distribution that is proper and iteratively reduces the total entropy of the distribution while maintaining the positivity and marginal properties. The result of this method is a highly localized, proper TFD.
This thesis will further explore and analyze the proposed minimum entropy algorithm. First, the minimum entropy algorithm and the concepts behind the algorithm will be introduced and discussed. After the introduction, a simple example of the method will be examined to help gain a basic understanding of the algorithm. Next, we will explore different rectangle selection methods which define the order in which the entropy of the distribution is minimized. We will then evaluate the effect of using different initial distributions with the minimum entropy algorithm. Afterwards, the results of the different rectangle selection methods and initial distributions will be analyzed and some more advanced concepts will be explored. Finally, we will draw conclusions and consider the overall effectiveness of the algorithm.
Bibliographical Information:

Advisor:Luis F. Chaparro; Patrick J. Loughlin; Amro El-Jaroudi

School:University of Pittsburgh

School Location:USA - Pennsylvania

Source Type:Master's Thesis

Keywords:electrical engineering

ISBN:

Date of Publication:06/09/2008