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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30 May 2006TL;DR: In this article, the authors presented an extraction method of environmental surface profile based on environmental modes using discrete Fourier transform (DFT) matrices as matrices transforming into environmental modes, which can be applied to a planar end-effector whose shape is an arbitrary polygon.
Abstract: It is very important for robots working in unknown environment to recognize surface profile of the environment. This paper presents an extraction method of environmental surface profile based on environmental modes. Contact condition between a planar end-effector and the environment is also determined by using active motion which is named "groping motion" of the end-effector. The extraction method utilizes discrete Fourier transform (DFT) matrices as matrices transforming into environmental modes. The proposed method can be applied to a planar end-effector whose shape is an arbitrary polygon. Moreover, a compliance controller for attitude of a planar end-effector with 3 supporting points is proposed to realize stable contact motion with unknown environment. The validity of the proposed method is shown by the experimental results
44 citations
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TL;DR: This tutorial simply reviews the DFT and FFT, with a few characteristic examples.
Abstract: Frequency analysis is an important issue in the IEEE. Using a computer in a calculation means moving into a non-physical, synthetic environment. Numerically, discrete or fast Fourier transformations (DFTs or FFTs) are used to obtain the frequency content of a time signal, and these are totally different than the mathematical definition of the Fourier transform. This tutorial simply reviews the DFT and FFT, with a few characteristic examples.
44 citations
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TL;DR: A fast and quasi-optimal algorithm for computing the NUDFT based on the fast Fourier transform (FFT) is proposed, which is essentially the FFT, and is competitive with state-of-the-art algorithms.
Abstract: By viewing the nonuniform discrete Fourier transform (NUDFT) as a perturbed version of a uniform discrete Fourier transform, we propose a fast and quasi-optimal algorithm for computing the NUDFT based on the fast Fourier transform (FFT). Our key observation is that an NUDFT and DFT matrix divided entry by entry is often well approximated by a low rank matrix, allowing us to express a NUDFT matrix as a sum of diagonally scaled DFT matrices. Our algorithm is simple to implement, automatically adapts to any working precision, and is competitive with state-of-the-art algorithms. In the fully uniform case, our algorithm is essentially the FFT. We also describe quasi-optimal algorithms for the inverse NUDFT and two-dimensional NUDFTs.
44 citations
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TL;DR: Some of the important features of the fast Fourier transform which are relevant to its increasing application to biomedical data are reviewed and a distinction is made between the power spectrum of ergodic signals, computed from the autocorrelation function, and the frequency spectrum of nonstationary biomedical signals.
Abstract: The fast Fourier transform (f.f.t.) is a powerful technique which facilitates analysis of signals in the frequency domain. This paper reviews some of the important features of the fast Fourier transform which are relevant to its increasing application to biomedical data. A distinction is made between the power spectrum of ergodic signals, computed from the autocorrelation function, and the frequency spectrum of nonstationary biomedical signals. The major practical pitfalls that are encountered in applying the f.f.t. technique to biomedical data are discussed, and practical hints for avoiding such pitfalls are suggested.
44 citations