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18. 2-D lnear Systems and Spectral Analysis - 2011

18. 2-D lnear Systems and Spectral Analysis - 2011 - EE 638...

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EE 638: Principles of Digital Color Imaging Systems Lecture 20: 2-D Linear Systems and Spectral Analysis
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Synopsis Special 2-D Signals 2-D Continuous-space Fourier Transform (CSFT) Linear, Shift-invariant Imaging Systems Periodic Structures
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Special 2-D Signals
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(Bassel function of 1 st kind order 1)
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2-D Impulse Function
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Sifting Property
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Spatial Frequency Components
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Spatial Domain Frequency Domain
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2-D CSFT Forward Transform: Inverse Transform:
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Hermitian Symmetry for Real Signals Let If f(x,y) is real, In this case, the inverse transform may be written as
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2-D Transform Relations 1. linearity 2. Scaling and shifting 3. Modulation 4. Reciprocity 5. Parseval’s Relation
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6. Initial value 7. Let then
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Separability A function is separable if it factors as: Some important separable functions:
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Important Transform Pairs 1. 2. 3. 4. 5. 6.
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