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Though any number of quantization levels is possible, common word lengths are 8-bit (256 levels), 16-bit (65,536 levels) and 24-bit (16.8 million levels). Quantizing a sequence of numbers produces a sequence of quantization errors which is sometimes modeled as an additive random signal called quantization noise because of its stochastic ...
Functions of space, time, or any other dimension can be sampled, and similarly in two or more dimensions. For functions that vary with time, let () be a continuous function (or "signal") to be sampled, and let sampling be performed by measuring the value of the continuous function every seconds, which is called the sampling interval or sampling period.
Vector quantization (VQ) is a classical quantization technique from signal processing that allows the modeling of probability density functions by the distribution of prototype vectors. Developed in the early 1980s by Robert M. Gray , it was originally used for data compression .
Simulation-based methods: Monte Carlo simulations, importance sampling, adaptive sampling, etc. General surrogate-based methods: In a non-instrusive approach, a surrogate model is learnt in order to replace the experiment or the simulation with a cheap and fast approximation. Surrogate-based methods can also be employed in a fully Bayesian fashion.
TV methods with iterative re-weighting have been implemented to reduce the influence of large gradient value magnitudes in the images. This has been used in computed tomography (CT) reconstruction as a method known as edge-preserving total variation. However, as gradient magnitudes are used for estimation of relative penalty weights between the ...
The sampling theory of Shannon can be generalized for the case of nonuniform samples, that is, samples not taken equally spaced in time. The Shannon sampling theory for non-uniform sampling states that a band-limited signal can be perfectly reconstructed from its samples if the average sampling rate satisfies the Nyquist condition. [ 1 ]
Conceptual approaches to sample-rate conversion include: converting to an analog continuous signal, then re-sampling at the new rate, or calculating the values of the new samples directly from the old samples. The latter approach is more satisfactory since it introduces less noise and distortion. [3] Two possible implementation methods are as ...
The sampling theory of Shannon can be generalized for the case of nonuniform sampling, that is, samples not taken equally spaced in time. The Shannon sampling theory for non-uniform sampling states that a band-limited signal can be perfectly reconstructed from its samples if the average sampling rate satisfies the Nyquist condition. [5]