A METHOD FOR EXTRACTING MAXIMUM RESOLUTION POWER SPECTRA FROM MICROWAVE SKY MAPS

A method for extracting maximal resolution power spectra from microwav e sky maps is presented and applied to the 2-yr COBE data, yielding a power spectrum that is consistent with a standard n=1, Q(rms-ps)=20 mu K model. By using weight functions that fall off smoothly near the Ga lactic cut, it is found that the spectral. resolution Delta l can be m ore than doubled at l=15 and more than tripled at l=20 compared to sim ply using Galaxy-cut spherical harmonics. For a future high-resolution experiment with reasonable sky coverage, the resolution around the co ld dark matter (CDM) Doppler peaks would be enhanced by a factor of ab out 100, down to Delta l similar to 1, thus allowing spectral features such as the locations of the peaks to be determined with great accura cy. The reason that the improvement is so large is basically that func tions with a sharp edge at the Galaxy cut exhibit considerable 'ringin g' in the Fourier domain, whereas smooth functions do not. The method presented here is applicable to any survey geometry, chopping strategy and exposure pattern whatsoever. The so-called signal-to-noise eigenf unction technique is found to be a special case, corresponding to igno ring the width of the window functions.