Topic

# Non-uniform discrete Fourier transform

About: Non-uniform discrete Fourier transform is a(n) research topic. Over the lifetime, 4067 publication(s) have been published within this topic receiving 123952 citation(s).

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IBM

^{1}TL;DR: In this article, the use of the fast Fourier transform in power spectrum analysis is described, and the method involves sectioning the record and averaging modified periodograms of the sections.

Abstract: The use of the fast Fourier transform in power spectrum analysis is described. Principal advantages of this method are a reduction in the number of computations and in required core storage, and convenient application in nonstationarity tests. The method involves sectioning the record and averaging modified periodograms of the sections.

8,370 citations

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01 Jan 1978

TL;DR: A comprehensive catalog of data windows along with their significant performance parameters from which the different windows can be compared is included, and an example demonstrates the use and value of windows to resolve closely spaced harmonic signals characterized by large differences in amplitude.

Abstract: This paper makes available a concise review of data windows and their affect on the detection of harmonic signals in the presence of broad-band noise, and in the presence of nearby strong harmonic interference. We also call attention to a number of common errors in the application of windows when used with the fast Fourier transform. This paper includes a comprehensive catalog of data windows along with their significant performance parameters from which the different windows can be compared. Finally, an example demonstrates the use and value of windows to resolve closely spaced harmonic signals characterized by large differences in amplitude.

6,731 citations

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01 Jan 1965

TL;DR: In this paper, the authors provide a broad overview of Fourier Transform and its relation with the FFT and the Hartley Transform, as well as the Laplace Transform and the Laplacian Transform.

Abstract: 1 Introduction 2 Groundwork 3 Convolution 4 Notation for Some Useful Functions 5 The Impulse Symbol 6 The Basic Theorems 7 Obtaining Transforms 8 The Two Domains 9 Waveforms, Spectra, Filters and Linearity 10 Sampling and Series 11 The Discrete Fourier Transform and the FFT 12 The Discrete Hartley Transform 13 Relatives of the Fourier Transform 14 The Laplace Transform 15 Antennas and Optics 16 Applications in Statistics 17 Random Waveforms and Noise 18 Heat Conduction and Diffusion 19 Dynamic Power Spectra 20 Tables of sinc x, sinc2x, and exp(-71x2) 21 Solutions to Selected Problems 22 Pictorial Dictionary of Fourier Transforms 23 The Life of Joseph Fourier

5,709 citations

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TL;DR: In this article, a discrete cosine transform (DCT) is defined and an algorithm to compute it using the fast Fourier transform is developed, which can be used in the area of digital processing for the purposes of pattern recognition and Wiener filtering.

Abstract: A discrete cosine transform (DCT) is defined and an algorithm to compute it using the fast Fourier transform is developed. It is shown that the discrete cosine transform can be used in the area of digital processing for the purposes of pattern recognition and Wiener filtering. Its performance is compared with that of a class of orthogonal transforms and is found to compare closely to that of the Karhunen-Loeve transform, which is known to be optimal. The performances of the Karhunen-Loeve and discrete cosine transforms are also found to compare closely with respect to the rate-distortion criterion.

4,205 citations

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Bell Labs

^{1}TL;DR: The Fourier transform data communication system is described and the effects of linear channel distortion are investigated and a differential phase modulation scheme is presented that obviates any equalization.

Abstract: The Fourier transform data communication system is a realization of frequency-division multiplexing (FDM) in which discrete Fourier transforms are computed as part of the modulation and demodulation processes. In addition to eliminating the bunks of subcarrier oscillators and coherent demodulators usually required in FDM systems, a completely digital implementation can be built around a special-purpose computer performing the fast Fourier transform. In this paper, the system is described and the effects of linear channel distortion are investigated. Signal design criteria and equalization algorithms are derived and explained. A differential phase modulation scheme is presented that obviates any equalization.

2,446 citations