Signal approximation using the bilinear transform

This thesis explores the approximation properties of a unique basis expansion. The expansion implements a nonlinear frequency warping between a continuous-time signal and its discrete-time representation according to the bilinear transform. Since there is a one-to-one mapping between the continuous-time and discrete-time frequency axes, the bilinear representation avoids any frequency aliasing distortions. We devote the first portion of this thesis to some theoretical properties of the bilinear representation, including the analysis and synthesis networks as well as bounds on the basis functions. These properties are crucial when we further analyze the bilinear approximation performance. We also consider a modified version of the bilinear representation in which the continuous-time signal is segmented using a short-duration window. This segmentation procedure affords greater time resolution and, in certain cases, improves the overall approximation quality. In the second portion of this thesis, we evaluate the approximation performance of the bilinear representation in two different applications. The first is approximating instrumental music. We compare the bilinear representation to a discrete cosine transform based approximation technique. The second application is computing the inner product of two continuous-time signals for a binary detection problem. In this case, we compare the bilinear representation with Nyquist sampling.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2007

Author dc:creator

• Venkataraman, Archana, Ph. D. Massachusetts Institute of Technology

Advisor dc:contributor.advisor

• Alan V. Oppenheim.

• Electrical Engineering and Computer Science.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/46466

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/46466