Covariance Between New Diagnostic Features: The Real and Imaginary Components of the Short time Fourier Transform

Covariance and the correlation coefficient between new diagnostic features, the real and imaginary components of the short time Fourier transform of the signal, were obtained for arbitrary stationary random signals. Obtained expressions take into account the significant parameters: the signal normalized autocovariance function, signal variance, duration of the short time Fourier transform, and Fourier transform frequency. Vibroacoustical diagnostics was considered using simultaneously new features and taking into account the covariance between features. It was shown that generally the power spectral density is not an optimal diagnostic feature and represents only a particular case of the proposed features.