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- W3100943674 abstract "Much of that which is ordinal is modelled as analog. Most computational engines, on the other hand, are digital. Transforming from analog to digital is straightforward: we simply sample. Regaining the original signal from these samples or assessing the information lost in the sampling process are the fundamental questions addressed by sampling and interpolation theory. This chapter deals with understanding, generalizing and extending the cardinal series of Shannon sampling theory. The fundamental form of this series states, remarkably, that a bandlimited signal is uniquely specified by its sufficiently close equally spaced samples. The cardinal series has many names, including the Whittaker-Shannon sampling theorem [514], the Whittaker-Shannon-Kotelnikov sampling theorem [679], and the Whittaker- Shannon-Kotelnikov-Kramer sampling theorem [679]. For brevity, we will use the terms sampling theorem and cardinal series. If a signal has finite energy, the minimum sampling rate is equal to two samples per period of the highest frequency component of the signal. Specifically, if the highest frequency component of the signal is B hertz, then the signal, x(t), can be recovered from the samples by The frequency B is also referred to as the signal’s bandwidth and, if B is finite, x(t) is said to be bandlimited [1283]." @default.
- W3100943674 created "2020-11-23" @default.
- W3100943674 creator A5064211368 @default.
- W3100943674 date "2009-01-22" @default.
- W3100943674 modified "2023-09-25" @default.
- W3100943674 title "The Sampling Theorem" @default.
- W3100943674 doi "https://doi.org/10.1093/oso/9780195335927.003.0010" @default.
- W3100943674 hasPublicationYear "2009" @default.
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