Topic
Discrete-time Fourier transform
About: Discrete-time Fourier transform is a research topic. Over the lifetime, 5072 publications have been published within this topic receiving 144643 citations. The topic is also known as: DTFT.
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TL;DR: The framework for signal processing on a spatial, or undirected, 2-D hexagonal lattice for both an infinite and a finite array of signal samples is developed, which includes the proper notions of z-transform, boundary conditions, filtering or convolution, spectrum, frequency response, and Fourier transform.
Abstract: We develop the framework for signal processing on a spatial, or undirected, 2-D hexagonal lattice for both an infinite and a finite array of signal samples. This framework includes the proper notions of z-transform, boundary conditions, filtering or convolution, spectrum, frequency response, and Fourier transform. In the finite case, the Fourier transform is called discrete triangle transform. Like the hexagonal lattice, this transform is nonseparable. The derivation of the framework makes it a natural extension of the algebraic signal processing theory that we recently introduced. Namely, we construct the proper signal models, given by polynomial algebras, bottom-up from a suitable definition of hexagonal space shifts using a procedure provided by the algebraic theory. These signal models, in turn, then provide all the basic signal processing concepts. The framework developed in this paper is related to Mersereau's early work on hexagonal lattices in the same way as the discrete cosine and sine transforms are related to the discrete Fourier transform-a fact that will be made rigorous in this paper
31 citations
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TL;DR: In this paper, generalized quantum key distribution schemes using spatially encoded $d$-dimensional qudits based on fractional Fourier transform operations are proposed, and the necessary conditions on the orders of the transforms which ensure a shared secret random key string and briefly discuss the transmission rate and a possible encoding procedure.
Abstract: We propose generalized quantum key distribution schemes using spatially encoded $d$-dimensional qudits based on fractional Fourier transform operations. We determine the necessary conditions on the orders of the transforms which ensure a shared secret random key string and briefly discuss the transmission rate and a possible encoding procedure. We also show that the fractional Fourier transform can be used to analyze more general eavesdropping strategies, including an intermediate-basis attack. The error rate and information gain for the intercept-resend and intermediate-basis attacks are briefly analyzed for a particular example. Effects of atmospheric turbulence in a free-space transmission are considered.
31 citations
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31 citations
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07 Nov 2004
TL;DR: In this article, a new approach for the identification and location of hot spots in proteins based on the short-time discrete Fourier transform (DFT) is proposed, which can identify hot spots by distinct peaks in the spectrum.
Abstract: A new approach for the identification and location of hot spots in proteins based on the short-time discrete Fourier transform (DFT) is proposed. In the new approach the short-time DFT of the protein numerical sequence is first computed and its columns are then multiplied by the DFT coefficients. By performing this step, the hot spot locations can be clearly identified by distinct peaks in the spectrum, thus achieving good localization in the amino acid domain.
30 citations
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05 Jun 2000TL;DR: A procedure called pruning, analogous to truncation of the singular-value decomposition, underlies a number of potential applications, among which the fast implementation of space-variant linear systems is discussed.
Abstract: We introduce the fractional Fourier domain decomposition for continuous and discrete signals and systems. A procedure called pruning, analogous to truncation of the singular-value decomposition, underlies a number of potential applications, among which we discuss the fast implementation of space-variant linear systems.
30 citations