M n a 0 0 0 0 e 0 1 1 1 b 1 0 1 1 f 1 1 2 0 i 0 2 2 2

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Unformatted text preview: gh it is straightforward to impose conditions on a given discrete signal spectra in order to avoid aliasing, it is not easy to do so for a general subsampling. • This depends on the shape of the spectra and the downsampling matrix . M n a 0 0 0 0 e 0 1 1 1 b 1 0 1 ‐1 f 1 1 2 0 i 0 2 2 2 c 2 0 2 ‐2 k 2 2 4 0 Ghassan AlRegib © Georgia Tech Ghassan AlRegib © Georgia Tech 17 Decimation ECE 6258 Fall 2012 Decimation ECE 6258 Fall 2012 • A necessary but not sufficient condition on the spectra support is that the areas must be less than . 1/ | det M | • One way to avoid aliasing is to apply a digital LPF with unity gain in its passband. The filter has to be chosen such that its spectra replication do not overlap when the filtered output signal (image) is downsampled. 18 Interpolation ECE 6258 Fall 2012 • To fill the inserted zero‐valued samples, we use interpolation. Recall in the 1D case we used Sinc function interpolation to do so. • The main idea is to relate the sampled image and the downsampled image to the continuous image. f [n ] f a [ Xn ] g[n ] f a [ XLn ] g[n] oversampled by a factor of | det L | Ghassan AlRegib © Georgia Tech 19 Ghassan AlRegib © Georgia Tec...
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This note was uploaded on 02/14/2014 for the course ECE 6258 taught by Professor Staff during the Fall '08 term at Georgia Tech.

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