Where does decimation collide?

In digital signal processing, decimation reduces the sampling rate of a discrete-time signal by an integer factor M, keeping every Mth sample and discarding the rest. To avoid aliasing, the signal is first low-pass filtered to below the new Nyquist limit, so decimation pairs an anti-alias filter with the downsampler. Crochiere and Rabiner's Multirate Digital Signal Processing and Oppenheim and Schafer's Discrete-Time Signal Processing develop the operation within multirate theory. The referent is a rate-conversion operation on a sampled signal, and despite the Latin root it has nothing to do with executing one soldier in ten.[1][2]

Unit

The decimation factor M and the resulting reduced sample rate

Recovery means

Not applicable

Measured by

Specified by the integer factor M, the anti-alias filter's cutoff and stopband attenuation, and the resulting Nyquist rate

In the real-space renormalization group, decimation is a coarse-graining transformation that removes (sums over) a chosen subset of the degrees of freedom on a lattice while leaving the rest, producing an effective system with renormalized couplings. Iterating the decimation generates a flow in coupling space whose fixed points govern critical behaviour. Goldenfeld's Lectures on Phase Transitions and the Renormalization Group sets out the decimation transformation and its use on spin chains and lattices. It is an operation on a statistical-mechanical model, unrelated to sample-rate reduction or military punishment beyond the shared idea of removing a fraction of elements.[3]

Unit

The renormalized couplings produced by integrating out a subset of sites or spins

Recovery means

Not applicable

Measured by

Tracked by the recursion relations for the couplings and the fixed points and critical exponents of the resulting RG flow