2012
DOI: 10.1002/cpa.21425
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Mathematics of Analog‐to‐Digital Conversion

Abstract: As the performance of digital circuits and the capacity of digital communication channels have advanced steadily over the past decades, digital signals have replaced analog signals in nearly every technological application domain, offering robustness, ever increasing quality, and speed. At the same time, many signals that we perceive audiovisually (sound and video), or measure via instrumentation (e.g., geophysical signals and medical images), are analog in their nature. Consequently, not only are the analog‐t… Show more

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Cited by 7 publications
(3 citation statements)
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“…Without loss of generality, we may assume x ∈ ∂A as otherwise x ∈ N t (∂A) trivially. First case is [DGWY10,Gün12]. The subfamily of piecewise affine automorphisms that have motivated this paper appear in the latter setting.…”
Section: Cs Güntürk and Nt Thaomentioning
confidence: 99%
“…Without loss of generality, we may assume x ∈ ∂A as otherwise x ∈ N t (∂A) trivially. First case is [DGWY10,Gün12]. The subfamily of piecewise affine automorphisms that have motivated this paper appear in the latter setting.…”
Section: Cs Güntürk and Nt Thaomentioning
confidence: 99%
“…The synthesis distortion can be seen as a generalized notion of linear discrepancy [18,24]. Recall (e.g.…”
Section: Introductionmentioning
confidence: 99%
“…By(19) and Proposition 4.2, this event occurs with probability at least 1 − e −2a 2 m − ε. With the simple bound σ m/k ≥ β −1 , we have σ min (V β, m,k Ẽk ) ≥ ε β √ k , and therefore the analysis distortion bound(18) with l = k yieldsD a (E, L) ≤ kε −1 δβ − m/k +1for any δ > 0 such that (β, δ) ∈ S µ,L . Now we specify the pair (β, δ) ∈ S µ,L .…”
mentioning
confidence: 98%