Discrete wavelet transform power spectrum estimator

A method for measuring the spectrum of a density field by the discrete wavelet transform (DWT) is studied. We show how the Fourier power spectrum can be detected by using the wavelet function coefficients (WFC) of the DWT. This method can successfully measure the power spectrum in samples for which traditional methods often fail because the samples are finite sized, have a complex geometry, or are varyingly sampled. We demonstrate that the spectrum features, such as the power law index, the magnitude, and the typical scales can be determined by the DWT reconstructed spectrum. We apply this method to analyze the power spectrum of the spatial distribution of the Ly-α clouds. The two popular data sets used for the spectrum detection have quite different geometries and samplings, yet the one-dimensional (1D) power spectra and their 3D reconstruction given by the DWT estimator show the same features. The analysis makes clear that the DWT estimator is a sensitive tool in revealing common and physical properties from diverse data sets.