Lattice Functions for the Analysis of Analog-to-Digital Conversion

Autor: Pablo Martinez-Nuevo, Alan V. Oppenheim
Rok vydání: 2019
Předmět:
Signal Processing (eess.SP)
FOS: Computer and information sciences
Bandlimiting
Computer science
Computer Science - Information Theory
Entire function
02 engineering and technology
Library and Information Sciences
Upper and lower bounds
30D20 (Primary) 30D15 (Secondary)
FOS: Electrical engineering
electronic engineering
information engineering
FOS: Mathematics
0202 electrical engineering
electronic engineering
information engineering
Nyquist–Shannon sampling theorem
Complex Variables (math.CV)
Electrical Engineering and Systems Science - Signal Processing
H.1.0
Signal processing
Mathematics - Complex Variables
Information Theory (cs.IT)
Quantization (signal processing)
Sampling (statistics)
020206 networking & telecommunications
Exponential type
Computer Science Applications
Amplitude
Analog signal
Algorithm
Information Systems
Interpolation
Zdroj: IEEE Transactions on Information Theory. 65:4915-4923
ISSN: 1557-9654
0018-9448
Popis: Analog-to-digital (A/D) converters are the common interface between analog signals and the domain of digital discrete-time signal processing. In essence, this domain simultaneously incorporates quantization both in amplitude and time, i.e. amplitude quantization and uniform time sampling. Thus, we view A/D conversion as a sampling process in both the time and amplitude domains based on the observation that the underlying continuous-time signals representing digital sequences can be sampled in a lattice---i.e. at points restricted to lie on a uniform grid both in time and amplitude. We refer to them as lattice functions. This is in contrast with the traditional approach based on the classical sampling theorem and quantization error analysis. The latter has been mainly addressed with the help of probabilistic models, or deterministic ones either confined to very particular scenarios or considering worst-case assumptions. In this paper, we provide a deterministic theoretical analysis and framework for the functions involved in digital discrete-time processing. We show that lattice functions possess a rich analytic structure in the context of integral-valued entire functions of exponential type. We derive set and spectral properties of this class of functions. This allows us to prove in a deterministic way and for general bandlimited functions a fundamental lower bound on the maximum frequency component introduced by quantization that is independent of the resolution of the quantizer.
9 pages, 5 figures, journal paper
Databáze: OpenAIRE
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