APPENDIX A
Continuous and Discrete Fourier Transforms
A.1 CONTINUOUS FOURIER TRANSFORM
Fourier transform is of fundamental importance in the analysis and design of linear systems. They express time or spatial-domain signals in the respective frequency domains. The continuous Fourier transform or simply the Fourier transform of a signal f(x) is defined as
where u is the frequency variable. If x is a spatial variable, then u is in cycles per unit distance. The inverse Fourier transform recovers the signal. Thus,
The extension of the 1-D Fourier transform ...
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