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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.
The term Nyquist Sampling Theorem (capitalized thus) appeared as early as 1959 in a book from his former employer, Bell Labs, [22] and appeared again in 1963, [23] and not capitalized in 1965. [24] It had been called the Shannon Sampling Theorem as early as 1954, [25] but also just the sampling theorem by several other books in the early 1950s.
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 ...
Digitization transforms continuous signals into discrete ones by sampling a signal's amplitude at uniform intervals and rounding to the nearest value representable with the available number of bits. This process is fundamentally inexact, and involves two errors: discretization error, from sampling at intervals, and quantization error, from ...
The equivalence of this inefficient method and the implementation described above is known as the first Noble identity. [6] [c] It is sometimes used in derivations of the polyphase method. Fig 1: These graphs depict the spectral distributions of an oversampled function and the same function sampled at 1/3 the original rate.
Related titles should be described in Quantization, while unrelated titles should be moved to Quantization (disambiguation). Quantization is the process of constraining an input from a continuous or otherwise large set of values (such as the real numbers ) to a discrete set (such as the integers ).
Data binning, also called data discrete binning or data bucketing, is a data pre-processing technique used to reduce the effects of minor observation errors.The original data values which fall into a given small interval, a bin, are replaced by a value representative of that interval, often a central value (mean or median).