Calculation of linear and nonlinear system responses from arbitrary deterministic and random excitations. Probability and joint probability distributions and methods of averaging. Concepts of correlations and Fourier analysis including DFT and FFT. Accuracy of measured data and its associated confidence level. Digital spectral analysis on finite length data record to extract system information through auto- and cross-correlations. Principles of window selections for periodic and non-periodic signals and window correction factors. Synthesis of correlated and uncorrelated noise sources.