Multidimensional sampling of isotropically bandlimited signals

Agrell, Erik, 1965 (author): Chalmers tekniska högskola,Chalmers University of Technology

Csébfalvi, Balázs (author): Budapesti Muszaki es Gazdasagtudomanyi Egyetem,Budapest University of Technology and Economics

(creator_code:org_t)

2018
2018
English.
In: IEEE Signal Processing Letters. - 1070-9908 .- 1558-2361. ; 25:3, s. 383-387

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Abstract Subject headings

A new lower bound on the average reconstruction error variance of multidimensional sampling and reconstruction is presented. It applies to sampling on arbitrary lattices in arbitrary dimensions, assuming a stochastic process with constant, isotropically bandlimited spectrum and reconstruction by the best linear interpolator. The lower bound is exact for any lattice at sufficiently high and low sampling rates. The two threshold rates where the error variance deviates from the lower bound gives two optimality criteria for sampling lattices. It is proved that at low rates, near the first threshold, the optimal lattice is the dual of the best sphere-covering lattice, which for the first time establishes a rigorous relation between optimal sampling and optimal sphere covering. A previously known result is confirmed at high rates, near the second threshold, namely, that the optimal lattice is the dual of the best sphere-packing lattice. Numerical results quantify the performance of various lattices for sampling and support the theoretical optimality criteria.

TEKNIK OCH TEKNOLOGIER -- Elektroteknik och elektronik -- Telekommunikation (hsv//swe)
ENGINEERING AND TECHNOLOGY -- Electrical Engineering, Electronic Engineering, Information Engineering -- Telecommunications (hsv//eng)
TEKNIK OCH TEKNOLOGIER -- Elektroteknik och elektronik -- Kommunikationssystem (hsv//swe)
ENGINEERING AND TECHNOLOGY -- Electrical Engineering, Electronic Engineering, Information Engineering -- Communication Systems (hsv//eng)
TEKNIK OCH TEKNOLOGIER -- Elektroteknik och elektronik -- Signalbehandling (hsv//swe)
ENGINEERING AND TECHNOLOGY -- Electrical Engineering, Electronic Engineering, Information Engineering -- Signal Processing (hsv//eng)

About the subject

ENGINEERING AND TECHNOLOGY: ENGINEERING AND ...; and Electrical Engin ...; and Telecommunicatio ...

ENGINEERING AND TECHNOLOGY: ENGINEERING AND ...; and Electrical Engin ...; and Communication Sy ...

ENGINEERING AND TECHNOLOGY: ENGINEERING AND ...; and Electrical Engin ...; and Signal Processin ...

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