## Spectral Effects in the Use of Newton?Cotes Approximations for Computing Discrete Fourier Transforms

Issue No. 08 - August (1971 vol. 20)

ISSN: 0018-9340

pp: 942-943

B.R. Hunt , Univ. Calif. Los Alamos Sci. Lab.

ABSTRACT

It is possible to view the discrete Fourier transform as the result of approximating the Fourier integral by a trapezoidal rule integration formula. In this correspondence the effects of using higher ordered Newton?Cotes integration formulas are examined. It is shown that in computing the spectrum of a bandlimited process, the trapezoidal rule is preferred when judged by the criterion of choosing the integration formula which leads to the coarsest sampling of the data.

INDEX TERMS

Aliasing of spectra, discrete Fourier transforms, Fourier, integral, Newton?Cotes quadrature formulas.

CITATION

B. Hunt, "Spectral Effects in the Use of Newton?Cotes Approximations for Computing Discrete Fourier Transforms," in

*IEEE Transactions on Computers*, vol. 20, no. , pp. 942-943, 1971.

doi:10.1109/T-C.1971.223378

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