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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08 Feb 2001
TL;DR: In this article, the authors define general properties of Fourier Transformer Transformer Transform, Discrete Fourier Transform, Fast Fourier transform, Laplace Transform, and Other Integral Transformer transform.
Abstract: I MATHEMATICAL FUNDAMENTALS: Basic Definitions General Properties of Fourier Transforms Discrete Fourier Transforms Fast Fourier Transforms Laplace and Other Integral Transforms II SPECTRAL APPLICATIONS: Fourier Transform Spectroscopy Fourier Transform Nuclear Magnetic Resonance (NMR) Spectrometry FT Ion Cyclotron Resonance Mass Spectrometry Diffraction and Fourier Transform Uncertainty Principle Signal Processing Fourier Self-Deconvolution Linear Prediction.
126 citations
TL;DR: A general transform that describes Fourier-family transforms, including the Fourier, short-time Fourier and S- transforms, is presented, allowing signals to be transformed in milliseconds rather than days, as compared to the original S-transform algorithm.
Abstract: Examining the frequency content of signals is critical in many applications, from neuroscience to astronomy. Many techniques have been proposed to accomplish this. One of these, the S-transform, provides simultaneous time and frequency information similar to the wavelet transform, but uses sinusoidal basis functions to produce frequency and globally referenced phase measurements. It has shown promise in many medical imaging applications but has high computational requirements. This paper presents a general transform that describes Fourier-family transforms, including the Fourier, short-time Fourier, and S- transforms. A discrete, nonredundant formulation of this transform, as well as algorithms for calculating the forward and inverse transforms are also developed. These utilize efficient sampling of the time-frequency plane and have the same computational complexity as the fast Fourier transform. When configured appropriately, this new algorithm samples the continuous S-transform spectrum efficiently and nonredundantly, allowing signals to be transformed in milliseconds rather than days, as compared to the original S-transform algorithm. The new and efficient algorithms make practical many existing signal and image processing techniques, both in biomedical and other applications.
126 citations
01 Jan 1986
TL;DR: The double Fourier decomposition of the sinogram is obtained by first taking the Fourier transform of each parallel-ray projection and then calculating the coefficients of a Fourier series with respect to angle for each frequency component of the transformed projections as discussed by the authors.
Abstract: The double Fourier decomposition of the sinogram is obtained by first taking the Fourier transform of each parallel-ray projection and then calculating the coefficients of a Fourier series with respect to angle for each frequency component of the transformed projections. The values of these coefficients may be plotted on a two-dimensional map whose coordinates are spatial frequency w (continuous) and angular harmonic number n (discrete). For |w| large, the Fourier coefficients on the line n=kw of slope k through the origin of the coefficient space are found to depend strongly on the contributions to the projection data that, for each view, come from a certain distance to the detector plane, where the distance is a linear function of k. The values of these coefficients depend only weakly on contributions from other distances from the detector. The theoretical basis of this property is presented in this paper and a potential application to emission computerized tomography is discussed.
125 citations
01 Jan 2008
TL;DR: In this paper, the FFT Algorithm with Radix-2 Decimation-in-Frequency (DIF) algorithm is presented, which is based on the Radix 2 Bit Reversal algorithm.
Abstract: This chapter contains sections titled: Introduction Development of the FFT Algorithm with Radix-2 Decimation-in-Frequency FFT Algorithm with Radix-2 Decimation-in-Time FFT Algorithm with Radix-2 Bit Reversal for Unscrambling Development of the FFT Algorithm with Radix-4 Inverse Fast Fourier Transform Programming Examples References
124 citations
TL;DR: The proposed sparse discrete fractional Fourier transform algorithm achieves multicomponent resolution in addition to its low computational complexity and robustness against noise and applies to the synchronization of high dynamic direct-sequence spread-spectrum signals.
Abstract: The discrete fractional Fourier transform is a powerful signal processing tool with broad applications for nonstationary signals. In this paper, we propose a sparse discrete fractional Fourier transform (SDFrFT) algorithm to reduce the computational complexity when dealing with large data sets that are sparsely represented in the fractional Fourier domain. The proposed technique achieves multicomponent resolution in addition to its low computational complexity and robustness against noise. In addition, we apply the SDFrFT to the synchronization of high dynamic direct-sequence spread-spectrum signals. Furthermore, a sparse fractional cross ambiguity function (SFrCAF) is developed, and the application of SFrCAF to a passive coherent location system is presented. The experiment results confirm that the proposed approach can substantially reduce the computation complexity without degrading the precision.
122 citations