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In measuring the power spectrum of the distribution of large numbers of darkmatter particles in simulations, or galaxies in observations, one has to useFast Fourier Transforms (FFT) for calculational efficiency. However, because ofthe required mass assignment onto grid points in this method, the measuredpower spectrum $\la |\delta^f(k)|^2\ra$ obtained with an FFT is not the truepower spectrum $P(k)$ but instead one that is convolved with a window function$|W(\vec k)|^2$ in Fourier space. In a recent paper, Jing (2005) proposed anelegant algorithm to deconvolve the sampling effects of the window function andto extract the true power spectrum, and tests using N-body simulations showthat this algorithm works very well for the three most commonly used massassignment functions, i.e., the Nearest Grid Point (NGP), the Cloud In Cell(CIC) and the Triangular Shaped Cloud (TSC) methods. In this paper, rather thantrying to deconvolve the sampling effects of the window function, we propose toselect a particular function in performing the mass assignment that canminimize these effects. An ideal window function should fulfill the followingcriteria: (i) compact top-hat like support in Fourier space to minimize thesampling effects; (ii) compact support in real space to allow a fast andcomputationally feasible mass assignment onto grids. We find that the scalefunctions of Daubechies wavelet transformations are good candidates for such apurpose. Our tests using data from the Millennium Simulation show that the truepower spectrum of dark matter can be accurately measured at a level better than2% up to $k=0.7k_N$, without applying any deconvolution processes. The newscheme is especially valuable for measurements of higher order statistics, e.g.the bi-spectrum,

An ideal mass assignment scheme for measuring the Power Spectrum with FFTs