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.
Papers published on a yearly basis
Papers
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TL;DR: The discrete Fourier transform of a time series is defined, some of its properties are discussed, the associated fast method for computing this transform is derived, and some of the computational aspects of the method are presented.
Abstract: The fast Fourier transform is a computational tool which facilitates signal analysis such as power spectrum analysis and filter simulation by means of digital computers. It is a method for efficiently computing the discrete Fourier transform of a series of data samples (referred to as a time series). In this paper, the discrete Fourier transform of a time series is defined, some of its properties are discussed, the associated fast method (fast Fourier transform) for computing this transform is derived, and some of the computational aspects of the method are presented. Examples are included to demonstrate the concepts involved.
471 citations
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TL;DR: In this paper, a new scheme is presented for the determination of the parameters that characterize a multifrequency signal, where the signal is weighted before the discrete Fourier transform (DFT) is calculated from which the frequencies and complex amplitudes of the various components of the signal are obtained by interpolation.
Abstract: A new scheme is presented for the determination of the parameters that characterize a multifrequency signal. The essential innovation is that the signal is weighted before the discrete Fourier transform (DFT) is calculated from which the frequencies and complex amplitudes of the various components of the signal are obtained by interpolation. It is shown that by using the Hanning window for tapering substantial improvements are achieved in the following respects: i) more accurate results are obtained for interpolated frequencies, etc., ii) harmonic interference is much less troublesome even if many tones with comparable strengths are present in the spectrum, iii) nonperiodic signals can be handled without an a priori knowledge of the tone frequencies. The stability of the new method with respect to noise and arithmetic roundoff errors is carefully examined.
440 citations
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01 Jan 1986TL;DR: The author describes the fast algorithm he discovered for spectral analysis and indeed any purpose to which Fourier Transforms and the Fast Fourier Transform are normally applied.
Abstract: The author describes the fast algorithm he discovered for spectral analysis and indeed any purpose to which Fourier Transforms and the Fast Fourier Transform are normally applied.
437 citations
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11 Mar 2005
TL;DR: In this article, the authors report on the work of I. I. Schoenberg and his students in the field of algebraic geometry, which is closely related to ours and has supplemented it in certain respects.
Abstract: Introduction. The material I am reporting on here was prepared in collaboration with I. I. Hirschman. It will presently appear in book form in the Princeton Mathematical Series. I wish also to refer at once to the researches of I. J. Schoenberg and his students. Their work has been closely related to ours and has supplemented it in certain respects. Let me call attention especially to an article of Schoenberg [5, p. 199] in this Bulletin where the whole field is outlined and the historical development is traced. In view of the existence of this paper I shall t ry to avoid any parallel development here. Let me take rather a heuristic point of view and concentrate chiefly on trying to entertain you with what seems to me a fascinating subject.
430 citations
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TL;DR: It is shown that the discrete equivalent of a chirp filter is needed to implement the computation of the discrete Fourier transform (DFT) as a linear filtering process, and that use of the conventional FFT permits the computations in a time proportional to N \log_{2} N for any N.
Abstract: It is shown in this paper that the discrete equivalent of a chirp filter is needed to implement the computation of the discrete Fourier transform (DFT) as a linear filtering process. We show further that the chirp filter should not be realized as a transversal filter in a wide range of cases; use instead of the conventional FFT permits the computation of the DFT in a time proportional to N \log_{2} N for any N, N being the number of points in the array that is transformed. Another proposed implementation of the chirp filter requires N to be a perfect square. The number of operations required for this algorithm is proportional to N^{3/2} .
410 citations