DFRFT: A Classified Review of Recent Methods with Its Application

In the literature, there are various algorithms available for computing the discrete fractional Fourier transform (DFRFT). In this paper, all the existing methods are reviewed, classified into four categories, and subsequently compared to find out the best alternative from the view point of minimal computational error, computational complexity, transform features, and additional features like security. Subsequently, the correlation theorem of FRFT has been utilized to remove significantly the Doppler shift caused due to motion of receiver in the DSB-SC AM signal. Finally, the role of DFRFT has been investigated in the area of steganography.

The Application of the Memory-Function Formalism to Dielectric Relaxation

The application of the memory-function formalism to dielectric relaxation is reconsidered. It is shown that the so-called Corresponding Micro-Macro Correlation theorem is not valid and that for a single macroscopic dielectric relaxation time, the single-molecule dipole correlation function may nevertheless be non-exponential. The deviations from the exponential decay for the single-molecule dipole correlation function are due to spatially dependent orientational correlations, and can at least partly be interpreted in terms of dielectric friction. The unsureness about these correlations implies that it is simpler to determine the rotational diffusion coefficient from the collective orientation correlation time as determined from dielectric measurements than from the single-molecule dipole correlation function as obtained from infrared spectroscopy.