Spectral estimation methods avoiding eigenvector decomposition

The autoregressive principal component technique uses the singular value decomposition (SVD) of an augmented dimension estimated autocorrelation matrix R to provide an accurate identification of frequencies in white noise. To avoid the eigen-decomposition of the matrix R, S.M. Kay and A.K. Shaw (1988) have applied a transformation on the inverse of R that truncates the eigenvalues associated with the noise. However, this technique requires the inversion of R and of another matrix. Two transformations that are applied directly to the matrix R are proposed. One is based on the matrix exponential and the other on component matrices. Another transformation analog to the MUSIC method without calculus of the eigenvectors is also proposed