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Regarding the decimation opoeration itself without any particular link to decimation filter, it's used in constructing filter banks, especially the most widespread dyadic filter banks. It's very actual in discrete wavelet transform (DWT), empirical mode decomposition (EMD), singular spectrum analysis (SSA). Such filter banks are formed in order to decompose the signal into a number of modes with different scale, thus performing the multiresolution analysis.
Desides, decimation is directed to changing the sampling frequency of the signal (decimation is opposite to interpolation).