Sampling a Digital Signal

Sampling data is the first step in the signal processing of wave forms coming from radar, submarine detection, earthquakes, seismic oil exploration, etc. Up-sampling and down-sampling are the basic operations in multirate discrete-time systems.
The bottom part of the figure shows up-sampling and down-sampling by an integer factor of the signal at the top. For the up-sampling process, equidistant zero-valued samples are inserted by the up-sampler between each consecutive sample of the input sequence .
Conversely, the down-sampling operation on the input sequence consists of keeping every sample of and removing the others.


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The up-sampled sequence is developed according to the input sequence :
The sampling rate of is times larger than that of the original sequence .
The down-sampled sequence is developed according to the input sequence :
Here the sampling rate of is that of the original sequence .
S. Mitra, Digital Signal Processing, 3rd ed., New York: McGraw-Hill, 2005.
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