In general, different lattices lead to discrete ambiguity functions having different States that 90◦ rotation ambiguity surfaces are invariant under two-dimensional Fourier transforms.Ī discrete ambiguity function is formed by sampling an ambiguity function over the points of a Setting f = g in Theorem A, we have the self-transform property of ambiguity surfaces that We will also work with the following generalization.Ī.f1 f2 /.u v/A∗. Of the two-dimensional Fourier transform on crossambiguity surfaces. The effort was unsuccessful but produced the following fundamental formula describing the action One goal of the above research was to provide a function-theoretic characterization of ambiguity We denote A.f f / by A.f / and call A.f / the autoambiguity or simply the ambiguity function R/, define the crossambiguity function of f and g by Referees for their careful reading of the manuscript and helpful suggestions.įor f g ∈ L2. The authors would like to express deep gratitude to Dr. The Department of Defense and was monitored by the Air Force Office of Scientific Research under contract numberį49620-90-C-0016. The research of the second author was supported by the Advanced Projects Agency of Of the Department of Defense and was monitored by the Air Force Office of Scientific Research under contract The research of the first author was supported by the Advanced Projects Agency When coupled with Poisson summation, these formulas lead toĮqually important lattice sum formulas that can be applied to the study of Weyl–Heisenberg systems.Īcknowledgements and Notes. Produced important formulas describing the action of the two-dimensional Fourier transform onĪuto- and crossambiguity surfaces. In the early 1960s, a major research effort was undertaken to establish the (narrowband)Īmbiguity function as a tool for radar signal synthesis. Parameters that yield the most snug frame at a stipulated density of basis functions. That appear simpler than those previously published and provide guidance in choosing lattice This condition leads to formulas for upper frame bounds Of the discrete ambiguity function of g over a lattice and properties of the Weyl–Heisenberg system Tight frames and for establishing an important relationship between l 1 -summability (condition A) Lattice sum formulas provide a framework for a new proof of a result of N. Of the discrete crossambiguity function of two signals f and g over a lattice with the inner product of the discrete autoambiguity functions of f and g over a “complementary” lattice. The theory of Weyl–Heisenberg systems, in the form of lattice sum formulas that relate the energy When coupled with the Poisson Summation formula, these results become applicable to In the early 1960s research into radar signal synthesis produced important formulasĭescribing the action of the two-dimensional Fourier transform on auto- and crossambiguity The Journal of Fourier Analysis and ApplicationsĪBSTRACT.
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