18Decimation

18Decimation - MAE 591 RANDOM DATA Decimation1 1. Downward...

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MAE 591 RANDOM DATA Decimation 1 1. Downward decimation: Downward decimation discards unwanted or redundant information with a corresponding compaction of the data. Filtering is usually performed in conjunction with decimation, and usually a low pass filter is employed. The filtering is done to prevent higher frequency data from becoming aliased and appearing as a lower frequency. Suppose that the original function is a cosine wave with frequency at 75% of the Nyquist folding frequency as shown below. The new function would appear, after decimation of every other points, to be much lower in frequency than the one from which it was derived. In particular, it would appear to be 25% of the original folding frequency. 0 2 4 6 8 10 12 14 16 every other point discarded 4 3 cos i x i π = -1 1 In order to prevent the higher-frequency information from appearing as low-frequency information, it is necessary to low pass filter in the following manner: Suppose the downward decimation index is p , so that the first point is kept, the next (
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18Decimation - MAE 591 RANDOM DATA Decimation1 1. Downward...

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