Fast Spherical Harmonic Analysis: a quick algorithm for generating and/or inverting full sky, high resolution CMB Anisotropy maps

We present a fast algorithm for generating full sky, high resolution ($\sim 5’$) simulations of the CMB anisotropy pattern. We also discuss the inverse problem, that of evaluating from such a map the full set of $a_{\mathrm{\ell }m}$'s and the spectral coefficients $C_{\mathrm{\ell }}$. 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.