Correlation windowing and spectral biasing in the design of noise generators having specified probability densities and power spectra

In the design of a nonlinear filtering system to generate a random process, z(t), with specified probability density function, p_z(.), and specified power spectral density, W_z(f), some combinations of p_z(.) and W_z(f) lead to violation of the positivity property of the power spectrum of the filter output. Three numerical spectral conditioning techniques (multiple windowing of the autocorrelation function, ´partial-raising/partial-lowering´ of the power spectrum and a combination of both) for finding minimum normalised mean squared error positive approximations to the required spectrum are described.