Topic

# Discrete Fourier transform

About: Discrete Fourier transform is a research topic. Over the lifetime, 10234 publications have been published within this topic receiving 207520 citations.

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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.

9,705 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.

7,130 citations

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24 Jan 2005

TL;DR: It is shown that such an approach can yield an implementation of the discrete Fourier transform that is competitive with hand-optimized libraries, and the software structure that makes the current FFTW3 version flexible and adaptive is described.

Abstract: FFTW is an implementation of the discrete Fourier transform (DFT) that adapts to the hardware in order to maximize performance. This paper shows that such an approach can yield an implementation that is competitive with hand-optimized libraries, and describes the software structure that makes our current FFTW3 version flexible and adaptive. We further discuss a new algorithm for real-data DFTs of prime size, a new way of implementing DFTs by means of machine-specific single-instruction, multiple-data (SIMD) instructions, and how a special-purpose compiler can derive optimized implementations of the discrete cosine and sine transforms automatically from a DFT algorithm.

5,172 citations

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01 Jan 1992TL;DR: This paper presents a meta-analysis of the Z-Transform and its application to the Analysis of LTI Systems, and its properties and applications, as well as some of the algorithms used in this analysis.

Abstract: 1. Introduction. 2. Discrete-Time Signals and Systems. 3. The Z-Transform and Its Application to the Analysis of LTI Systems. 4. Frequency Analysis of Signals and Systems. 5. The Discrete Fourier Transform: Its Properties and Applications. 6. Efficient Computation of the DFT: Fast Fourier Transform Algorithms. 7. Implementation of Discrete-Time Systems. 8. Design of Digital Filters. 9. Sampling and Reconstruction of Signals. 10. Multirate Digital Signal Processing. 11. Linear Prediction and Optimum Linear Filters. 12. Power Spectrum Estimation. Appendix A. Random Signals, Correlation Functions, and Power Spectra. Appendix B. Random Numbers Generators. Appendix C. Tables of Transition Coefficients for the Design of Linear-Phase FIR Filters. Appendix D. List of MATLAB Functions. References and Bibliography. Index.

3,911 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.

2,507 citations