Topic
Non-uniform discrete Fourier transform
About: Non-uniform discrete Fourier transform is a research topic. Over the lifetime, 4067 publications have been published within this topic receiving 123952 citations.
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01 Jan 2001
TL;DR: The robustness of NDFT algorithms with respect to roundoff errors is discussed, and approximative methods for the fast computation of multivariate discrete Fourier transforms for nonequispaced data are considered.
Abstract: In this chapter we consider approximativemethods for the fast computation of multivariate discrete Fourier transforms for nonequispaced data (NDFT) in the time domain and in the frequency domain. In particularwe are interested in the approximation error as function of the arithmetic complexity of the algorithm. We discuss the robustness of NDFTiaalgorithms with respect to roundoff errors and applyNDFTalgorithms for the fast computation of Besseltransforms.
321 citations
Book•
11 Feb 1983
TL;DR: This chapter discusses Fourier Series and Fourier Transform Algorithms, Discrete Fourier Transforms, DFT Filter Shapes and Shaping, and Spectral Analysis Using the FFT.
Abstract: Preface. Acknowledgments. List of Acronyms. Notation. Introduction. Fourier Series and Fourier Transform. Discrete Fourier Transforms. Fast Fourier Transform Algorithms. FFT Algorithms That Reduce Multiplications. DFT Filter Shapes and Shaping. Spectral Analysis Using the FFT. Walsh-Hadamard Transforms. The Generalized Transform. Discrete Orthogonal Transforms. Number Theoretic Transforms. Appendix. References. Index.
320 citations
TL;DR: In this paper, a data-compensated discrete Fourier transform is proposed to estimate the power spectrum of a time series formed with unequally spaced observations, which is defined so as to include the uneven spacing of the dates of observation and weighting of corresponding data.
Abstract: A better estimation of the power spectrum of a time series formed with unequally spaced observations may be obtained by means of a data-compensated discrete Fourier transform. This transform is defined so as to include the uneven spacing of the dates of observation and weighting of the corresponding data. The accurate determination of the peak heights allows one to design harmonic filters and thus to make a more certain choice among peaks of similar height and also to discriminate peaks that are just aliases of other peaks. The theory is applied to simulated time series and also to true observational data.
320 citations
TL;DR: A new structure and a simplified interpretation of short-time Fourier synthesis using synthesis windows is presented and it is shown how this structure can be used for analysis/synthesis applications which require different analysis and synthesis rates, such as time compression or expansion.
Abstract: In this correspondence we present a new structure and a simplified interpretation of short-time Fourier synthesis using synthesis windows. We show that this approach can be interpreted as a modification of the overlap-add method where we inverse the Fourier transform and window by the synthesis window prior to overlap-adding. This simplified interpretation results in a more efficient structure for short-time synthesis when a synthesis window is desired. In addition, we show how this structure can be used for analysis/synthesis applications which require different analysis and synthesis rates, such as time compression or expansion.
315 citations
Book•
13 Dec 1994
TL;DR: The Discrete Fourier Transform (DFT) as mentioned in this paper is a Fourier transform based on the Fourier Integral Transform (FIFO) and is used as an estimator of the FFT.
Abstract: CONTINUOUS FOURIER ANALYSIS. Background. Fourier Series for Periodic Functions. The Fourier Integral. Fourier Transforms of Some Important Functions. The Method of Successive Differentiation. Frequency-Domain Analysis. Time-Domain Analysis. The Properties. The Sampling Theorems. DISCRETE FOURIER ANALYSIS. The Discrete Fourier Transform. Inside the Fast Fourier Transform. The Discrete Fourier Transform as an Estimator. The Errors in Fast Fourier Transform Estimation. The Four Kinds of Convolution. Emulating Dirac Deltas and Differentiation on the Fast Fourier Transform. THE USER'S MANUAL FOR THE ACCOMPANYING DISKS. Appendices. Answers to the Exercises. Index.
309 citations