Principal components analysis of the short-time Fourier transform

The authors introduce a novel time-frequency representation, the principal short-time Fourier transform (PSTFT), as a reduced-data characterization of the nonstationary spectral content of a sequence. To form the PSTFT, the authors apply principal components analysis to STFT frequency slices and retain only the first principal component information. This information alone allows for exact reconstruction of the original sequence from its PSTFT representation. The PSTFT retains explicit information about the nonstationary spectral content of a sequence, as well as implicit information necessary for reconstruction of the sequence. The results obtained are extended to other time-frequency distributions, which include the Wigner-Ville distribution, the complex energy density, and the radar ambiguity function