On Digital Signal Processing of Time Series for Spectrum Estimation

We present a study of power spectral density (PSD) estimation from data sampled in the time domain. This work was motivated by our recent development of digital radiometry, where radiation spectra were obtained by processing the digitally sampled signal. The PSD estimation can be generalized by a quadratic estimator and the minimization of the mean squared error (mse) of the estimator leads to the optimal window choice. The bounds of the variance and the bias are formulated in order to quantify the uncertainty associated with nonideal PSD estimation in digital signal processing (DSP). Windowed estimates of spectrum measurements are presented for comparison in terms of computational efficiency and amplitude measurement precision. A few examples of real and simulated data are shown for comparison.