Solutions for Chapter 4: Signal Processing and Receivers: Theory

  • Thomas L. Wilson
  • Susanne Hüttemeister
Part of the Astronomy and Astrophysics Library book series (AAL)


We must evaluate the integral \(\int _{-\infty }^{+\infty } A \mathrm {e}^{-x^2/2\sigma ^2}\mathrm {d}x=1\). The standard approach is to evaluate the square of this integral in terms of the variables x and y. Then we have \(A^2 \int _{-\infty }^{+\infty } \mathrm {e}^{-x^2/2\sigma ^2} \mathrm {d}x \int _{-\infty }^{+\infty } \mathrm {e}^{-y^2/2\sigma ^2}\mathrm {d}y=1\). Now transform from rectangular to two-dimensional polar coordinates, so that

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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Thomas L. Wilson
    • 1
  • Susanne Hüttemeister
    • 2
  1. 1.Max-Planck-Institut für RadioastronomieBonnGermany
  2. 2.Zeiss-Planetarium BochumBochumGermany

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