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The purpose of our study is to understand the mathematical origin in realspace of modulated and damped sinusoidal peaks observed in cosmic microwavebackground radiation anisotropies. We use the theory of the Fourier transformto connect localized features of the two-point correlation function in realspace to oscillations in the power spectrum. We also illustrate analyticallyand by means of Monte Carlo simulations the angular correlation function fordistributions of filled disks with fixed or variable radii capable ofgenerating oscillations in the power spectrum. While the power spectrum showsrepeated information in the form of multiple peaks and oscillations, theangular correlation function offers a more compact presentation that condensesall the information of the multiple peaks into a localized real space feature.We have seen that oscillations in the power spectrum arise when there is adiscontinuity in a given derivative of the angular correlation function at agiven angular distance. These kinds of discontinuities do not need to be abruptin an infinitesimal range of angular distances but may also be smooth, and canbe generated by simply distributing excesses of antenna temperature in filleddisks of fixed or variable radii on the sky, provided that there is a non-nullminimum radius and/or the maximum radius is constrained.

Peaks in the CMBR power spectrum. I. Mathematical analysis of the associated real space features