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In digital signal processing, downsampling, compression, and decimation are terms associated with the process of resampling in a multi-rate digital signal processing system. Both downsampling and decimation can be synonymous with compression , or they can describe an entire process of bandwidth reduction ( filtering ) and sample-rate reduction.
The length of the impulse response of the filter in method 1 corresponds to the number of points used in interpolation in method 2. In method 1, a slow pre-computation (such as the Remez algorithm) can be used to obtain an optimal (per application requirements) filter design. Method 2 will work in more general cases, e.g. where the ratio of ...
The bandwidth, B, in this example is just small enough that the slower sampling does not cause overlap (aliasing). Sometimes, a sampled function is resampled at a lower rate by keeping only every M th sample and discarding the others, commonly called "decimation". Potential aliasing is prevented by lowpass-filtering the samples before decimation.
Lanczos windows for a = 1, 2, 3. Lanczos kernels for the cases a = 1, 2, and 3, with their frequency spectra. A sinc filter would have a cutoff at frequency 0.5. The effect of each input sample on the interpolated values is defined by the filter's reconstruction kernel L(x), called the Lanczos kernel.
Recall that decimation of sampled data in one domain (time or frequency) produces overlap (sometimes known as aliasing) in the other, and vice versa. Compared to an -length DFT, the summation/overlap causes decimation in frequency, [1]: p.558 leaving only DTFT samples least affected by spectral leakage.
If one draws the data-flow diagram for this pair of operations, the (x 0, x 1) to (y 0, y 1) lines cross and resemble the wings of a butterfly, hence the name (see also the illustration at right). A decimation-in-time radix-2 FFT breaks a length-N DFT into two length-N/2 DFTs followed by a combining stage consisting of many butterfly operations.
is the number of samples per stage (usually 1 but sometimes 2), and N {\displaystyle N} is the order: the number of comb-integrator pairs. The numerator comes from multiplying N {\displaystyle N} negative feedforward comb stages (each is simply multiplication by 1 − z − R M {\displaystyle 1-z^{-RM}} in the z-domain).
Decimation is the process of reducing sample rate. Decimation originally meant "take one sample in every 10", but later this term was generalized to simply mean any reduction in sample rate. This electronics-related article is a stub .