Abstract
We employ the one-dimensional Fourier representation (1DFR) to analyse the three-year WMAP de-biased internal linear combination (DILC) map and its possible contamination with galactic foregrounds. The 1DFR is a representation of the spherical harmonic coefficients for each ℓ mode using an inverse Fourier transform into one-dimensional curves. On the basis of the a priori assumption that the cosmic microwave background signal should be statistically independent of, and consequently have no significant correlation with, any foregrounds, we cross correlate the 1DFR curves of 2 ≤ ℓ ≤ 10 modes, which are claimed by the WMAP team to be free of contamination and suitable for whole-sky analysis. We find that eight out of the nine modes are negatively cross correlated with the foreground maps, an event which has a probability of only 9/512 ≃ 0.0176 for uncorrelated signals. Furthermore, the local extrema of the 1DFR curves between the DILC and those of the foregrounds for ℓ = 2 and 6 are correlated with significance level below 0.04. We also discuss the minimum variance optimization method and use the properties of the measured cross correlation to estimate the possible level of contamination present in the DILC map.