On the Estimation of Power Spectral Densities of Discontiguous Solar Wind Turbulence Signals

Spectral and correlation analyses are essential tools to investigate the turbulent properties of the solar wind from in-situ spacecraft observations. Most of these statistical techniques are based on estimators of autocorrelation functions (ACF) and power spectral densities (PSD). The PSD is often estimated as the squared amplitude of the fast Fourier transform (FFT), which normally requires uniformly-spaced, contiguous data. However, spacecraft data often have missing points that need to be filled in before applying the FFT, commonly with linear interpolation. Data gaps become a bigger problem when conditioning is applied to the signal and many gaps are introduced to cover sections of the signal with undesirable properties. The PSD is also related to the ACF via the Wiener-Khinchin theorem. The advantage of the ACF is that is it possible to obtain estimators that are resilient to data gaps without the need for interpolation. In this work, we artificially introduce gaps to synthetic signals obtained from numerical simulations of steadily-driven, homogeneous Magnetohydrodynamic (MHD) turbulence and to high resolution Wind magnetic field signals to investigate the consistency (convergence to its true ensemble-averaged counterpart) of a new PSD estimator for discontiguous signals and its sensitivity to the total gap percentages (TGP). This conditioned estimator for the PSD is then applied to conditioned Wind data to study spectral and correlation properties of the slow solar wind, which allows us to use a larger statistical sample than conventional FFT methods.