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: This work reports the extension of concentric ring sampling for 3-D NMR experiments as Randomized Concentric Shell Sampling (RCSS), where sampling points for the indirect dimensions are positioned on concentric shells, and random rotations in the angular space are used to avoid coherent artifacts.
Abstract: Recent efforts to reduce the measurement time for multidimensional NMR experiments have fostered the development of a variety of new procedures for sampling and data processing. We recently described concentric ring sampling for 3-D NMR experiments, which is superior to radial sampling as input for processing by a multidimensional discrete Fourier transform. Here, we report the extension of this approach to 4-D spectroscopy as Randomized Concentric Shell Sampling (RCSS), where sampling points for the indirect dimensions are positioned on concentric shells, and where random rotations in the angular space are used to avoid coherent artifacts. With simulations, we show that RCSS produces a very low level of artifacts, even with a very limited number of sampling points. The RCSS sampling patterns can be adapted to fine rectangular grids to permit use of the Fast Fourier Transform in data processing, without an apparent increase in the artifact level. These artifacts can be further reduced to the noise level using the iterative CLEAN algorithm developed in radioastronomy. We demonstrate these methods on the high resolution 4-D HCCH-TOCSY spectrum of protein G’s B1 domain, using only 1.2% of the sampling that would be needed conventionally for this resolution. The use of a multidimensional FFT instead of the slow DFT for initial data processing and for subsequent CLEAN significantly reduces the calculation time, yielding an artifact level that is on par with the level of the true spectral noise.
80 citations
01 May 1982
TL;DR: This paper presents various conditions that are sufficient for reconstructing a discrete-time signal from samples of its short-time Fourier transform magnitude, for applications such as speech processing.
Abstract: This paper presents various conditions that are sufficient for reconstructing a discrete-time signal from samples of its short-time Fourier transform magnitude. For applications such as speech processing, these conditions place very mild restrictions on the signal as well as the analysis window of the transform. Examples of such reconstruction for speech signals are included in the paper.
79 citations
TL;DR: In this article, the authors compare the finite Fourier (-exponential) and Fourier-Kravchuk transform, which is a canonical transform whose fractionalization is well defined.
79 citations
TL;DR: The theoretical basis of the selective Fourier transform technique is developed and experimental results are presented, including comparisons of spectral localization using either the selective fourier transform method or conventional multidimensional Fouriertransform chemical‐shift imaging.
Abstract: We have introduced the selective Fourier transform technique for spectral localization. This technique allows the acquisition of a high-resolution spectrum from a selectable location with control over the shape and size of the spatial response function. The shape and size of the spatial response are defined during data acquisition and the location is selectable through processing after the data acquisition is complete. The technique uses pulsed-field-gradient phase encoding to define the spatial coordinates. In this paper the theoretical basis of the selective Fourier transform technique is developed and experimental results are presented, including comparisons of spectral localization using either the selective Fourier transform method or conventional multidimensional Fourier transform chemical-shift imaging. © Academic Press, Inc.
79 citations
TL;DR: In this paper, a spectral approach is developed to solve the elasto-static equations of field dislocation and g-disclination mechanics in periodic media, which is consistent with the pixel grid for the calculation of first and second order spatial derivatives, and compared to the classical discrete approximation of continuous Fourier transforms when deriving elastic fields of defects.
79 citations