Square-wave Fourier transform

Bates, R. H. T.; Napier, P. J.; Chang, Yuan

doi:10.1049/el:19700513

Cited by 4 publications

(1 citation statement)

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“…The FFT actually computes a discrete Fourier series, but may be used to approximate a continuous Fourier integral using sampled data. It has been shown (Hunt 1971 ) that the discrete Fourier transform of sampled data, as computed by the FFT, is equivalent to a trapezoidal approximation to the Fourier integral, and that the Fourier transform computed in this manner is more accurate than that evaluated using a higher order interpolation scheme on the data, provided that there is no aliasing (Bates et al 1970 ) .…”

Section: Discussionmentioning

confidence: 99%

Image Reconstruction from Projections

Herman

1979

Topics in Applied Physics

207

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The problem of reconstructing cross-sections from their projections, using Fourier transform processing, is considered in detail and is related to problems in medical tomography. A number of equations relating cross-sections to their projections are derived, and are used as the bases for algorithms which enable cross-sections to be reconstructed from a finite number of projections. Results of computations on analytically derived and radiographically measured projections demonstrate the usefulness of these techniques. A proposal for a new type of transverse tomographic system is described. It is demonstrated that images of crosssections may be restored from tomograms produced using this system, by the use of both optical and digital processing techniques. Image reconstruction techniques using Fourier transforms are shown to be of use for reconstructing three-dimensional radio-isotope distribution~ from scintigraphic projections measured with a gamma camera.

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Section: Discussionmentioning

confidence: 99%