A theory of nonlinear systems

Introduction: A physically realizable nonlinear system, like a linear one, is a system whose present output is a function of the past of its input. We may regard the system as a computer that operates on the past of one time function to yield the present value of another time function. Mathematically we say that the system performs a transformation on the past of its input to yield its present output. When this transformation is linear (the case of linear systems) we can take advantage of the familiar convolution integral to obtain the present output from the past of the input and the system is said to be characterized by its response to an impulse. That is, the response of a linear system to an impulse is sufficient to determine its response to any input. When the transformation is nonlinear we no longer have a simple relation like the convolution integral relating the output to the past of the input and the system can no longer be characterized by its response to an impulse since superposition does not apply. Wiener has shown, however, that we can characterize a nonlinear system by a set of coefficients and that these coefficients can be determined from a knowledge of the response of the system to shot noise excitation. Thus, shot noise occupies the same position as a probe for investigating nonlinear systems that the impulse occupies as a probe for investigating linear systems. The first section of this thesis is devoted to the Wiener theory of nonlinear system characterization. Emphasis is placed on important concepts of this theory that are used in succeeding chapters to develop a theory for determining optimum nonlinear systems.

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Electrical Engineering

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

1956

Author dc:creator

• Bose, Amar G

Advisor dc:contributor.advisor

• Y.W. Lee.

• Electrical Engineering.

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/1721.1/38918

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/38918