A large class of signals can be conveniently modeled by a stationary first-order Markoff process. This paper shows that for such a process the elements of the covariance matrix in the discrete Fourier transform domain can be calculated in closed form which facilitates a direct comparison of the transform with the discrete Karhunen-Loéve transform of KLT. A similar technique is applied to the analysis of the discrete consine transform or DCT. Both transforms are shown to be asymptotically equivalent to the KLT, i.e., they become equivalent to it as the block size or the number of sample points approaches infinity. Significant conclusions in this paper are that in the DCT domain the residual correlation is surprisingly smaller than in the DFT domain even for a nominal block size and that the decorrelation by the DCT is relatively immune to statistics change.

The reliability of the FE method and the CV method for determining the localized state distribution N(E) in GD a-Si are evaluated by computer simulation. It is shown that calculation by the CV method is almost exact and the FE method is less reliable. But the FE method may be more reliable than the CV method about the accuracy of measured values. The new calculation method combining both methods and the iteration method are suggested for obtaining almost true distribution N(E). And the effect of surface states on calculation of N(E) is evaluated; the allowable surface state density is shown to be below 1011cm-2eV-1. The effect of the Fermi-Dirac distribution function F(E) at room temperature is estimated. The results indicate that correction by room temperature F(E) is necessary.