Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-28T02:56:47.522Z Has data issue: false hasContentIssue false
  • English
  • Français

Extending the Fourier Transform – The Positivity Constraint

Published online by Cambridge University Press:  12 April 2016

M.M. Komesaroff  and
I. Lerche
M.M. Komesaroff
Affiliation:
Division of Radiophysics, CSIRO, Sydney, Australia
I. Lerche
Affiliation:
Division of Radiophysics, CSIRO, Sydney, Australia

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In radio astronomy it is often necessary to estimate a brightness distribution from a limited number of samples of its Fourier transform. The manifest requirement that the brightness distribution be everywhere positive imposes definite constraints on its Fourier transform which yield information about unmeasured Fourier components. Here we discuss the question: given the first n+1 values, p0, P1 … pn, of a uniformly sampled Fourier transform of a real positive function, what can we say about Fourier terms of higher order?

Type
Part V: Maximum Entropy Image Reconstruction
Information
International Astronomical Union Colloquium , Volume 49: Image Formation from Coherence Functions in Astronomy , 1979 , pp. 241 - 247
Copyright
Copyright © Reidel 1979

References

Ables, J.: 1974, Astron. Astrophys. Suppl. 15, p. 383.Google Scholar
Burg, J.P.: 1967, Maximum Entropy Spectral Analysis – paper presented at 37th Annual International SEG Meeting, Oklahoma City.Google Scholar
Komesaroff, M.M., and Lerche, I.: 1978 – to be submitted to J. Math. Phys.Google Scholar
Newman, W.I.: 1977, Astron. Astrophys. 54, p. 369.Google Scholar
Van den Bos, A.: 1971, IEEE Trans. Inf. Theory 17, p. 493.CrossRefGoogle Scholar