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2 - Linear Invariant Systems and Fourier Analysis

Published online by Cambridge University Press:  22 December 2022

Yaping Zhang  and
Ting-Chung Poon
Yaping Zhang
Affiliation:
Kunming University of Science and Technology, China
Ting-Chung Poon
Affiliation:
Virginia Polytechnic Institute and State University
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Summary

The purpose of this chapter is twofold. We will first discuss basic aspect of signals and linear systems in the first part. As we will see in subsequent chapters that diffraction as well as optical imaging systems can be modelled as linear systems. In the second part, we introduce the basic properties of Fourier series, Fourier transform as well as the concept of convolution and correlation. Indeed, many modern optical imaging and processing systems can be modelled with the Fourier methods, and Fourier analysis is the main tool to analyze such optical systems. We shall study time signals in one dimension and signals in two dimensions will then be covered. Many of the concepts developed for one-dimensional (1-D) signals and systems apply to two-dimensional (2-D) systems. This chapter also serves to provide important and basic mathematical tools to be used in subsequent chapters.

Keywords

linear and time-invariant systemsfrequency resposne functionsFourier analysisFourier series2-D Fourier trasnformsproperties of Fourier transformConvolutioncorrelationmatching filtering
Type
Chapter
Information
Modern Information Optics with MATLAB , pp. 21 - 69
Publisher: Cambridge University Press
Print publication year: 2023

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References

Banerjee, P. P. and Poon, T.-C. (1991). Principles of Applied Optics. Irwin, Illinois.Google Scholar
Blahut, R. (2004). Theory of Remote Image Formation. Cambridge University Press, Cambridge.Google Scholar
Lathi, B. P. and Green, R. (2018). Linear Systems and Signals, 3rd ed., Oxford University Press, Oxford.Google Scholar
Poon, T.-C. (2007). Optical Scanning Holography with MATLAB®. Springer, New York.CrossRefGoogle Scholar
Poon, T.-C. and Kim, T. (2018). Engineering Optics with MATLAB®, 2nd ed., World Scientific, New Jersey.Google Scholar
Ulaby, F. T. andYagle, A. E. (2016). Engineering Signals and Systems in Continuous and Discrete Time, 2nd ed., National Technology & Science Press.Google Scholar

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