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Unformatted text preview: ng, in general, is understood to mean the representation of a discrete version of a continuous signal. But if we select subsamples from an already sampled image, then we are performing sampling as well. g[n] f [ Mn] • g[n] contains every Mth sample of [ n ] f 1 M g[ n ] Sampling density of sampling density of f [ n ] Ghassan AlRegib © Georgia Tech 7 Ghassan AlRegib © Georgia Tech 8 2 9/11/2012 Downsampling ECE 6258 Fall 2012 • 2‐D: In rectangular downsampling: ECE 6258 Fall 2012 General 2‐D Subsampling • Let be the downsampling matrix M g[ n ] f [ Mn ] g[n] f [ Mm, Nn] i.e. Keeping every Mth sample of every Nth row • Sampling density is reduced by a factor of | det M | 1 g[m, n] Sampling density of MN sampling density of f [m, n] M • Note: A dowsampled image by is considered as a sampled image of the continuous image by M Ghassan AlRegib © Georgia Tech ECE 6258 Fall 2012 9 General 2‐D Subsampling Ghassan AlRegib © Georgia Tech 10 Example ECE 6258 Fall 2012 1 1 M 1 1 is equivalent to Rotation 1 1 m mn g[m, n] f f 1 1 n m n Ghassan AlRegib © Georgia Tech 11 Ghassan AlRegib © Georgia Tech 12 3 9/11/2012 Downsampling ECE 6258 Fall 2012 • To find the relation between the spectra of both signals, we relate them to the analog signals: F (...
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