Fast Spherical Harmonic Analysis: A Quick Algorithm for Generating and/or InvertingFull-Sky, High-Resolution Cosmic Microwave Background Anisotropy Maps

We present a fast algorithm for generating full sky, high resolution (\ 5') simulations of the CMB anisotropy pattern. We also discuss the inverse problem, that of evaluating from such a map the full set of a\ ₌'s and the spectral coefficients C_\. We show that using an Equidistant Cylindrical Projection of the sky substantially speeds up the calculations. Thus, generating and/or inverting a full sky, high resolution map can be easily achieved with present day computer technology.