The fractional Fourier transformation is used to transform the rectangular Gabor lattice into a quin-cunx lattice. By using the isometric property of the unitary fractional Fourier transformation, the biorthog-onality relation for the rectangular lattice is transformed into a relation which holds for the quincunx lattice. Since a Gaussian function, which plays an important role as a window func...

The original definition of the derivatives of a function makes sense only for integral orders, i.e. we can speak of the first or second derivative and so on. However, it is possible to extend the definition of the derivative to noninteger orders by using an elementary property of Fourier transforms. Bracewell shows how fractional derivatives can be used to characterize the discontinuities of ce...

In this article, an image feature extraction method based on two-dimensional (2D) Mellin cepstrum is introduced. The concept of one-dimensional (1D) mel-cepstrum that is widely used in speech recognition is extended to two-dimensions using both the ordinary 2D Fourier transform and the Mellin transform. The resultant feature matrices are applied to two different classifiers such as common matri...

The photoswitching behavior of the polyacrylic acid (PAA) doped by methyl orange (MO) brush film was investigated using spectral analysis UV-Vis absorbance, Fourier Transformation Infrared spectroscopy, 2D electrical conductivity mapping and Atomic Force Microscopy. kinetics time evolution photoisomerization PAA-MO PEBs from E-state to Z-state UV-light irradiation, reverse thermal relaxation ex...

Hypercomplex or quaternions numbers have been used recently for both greyscale and colour image processing. Fast, numerous hypercomplex 2D Fourier transforms were presented as a generalization of the complex 2D Fourier transform to this new hypercomplex space. Thus, the major problem was to put an interpretation of what information the Fourier coefficients could provide. In this paper, we first...

We propose the adaptive S-method-based technique for imaging of SAR and ISAR targets. This approach can be applied in the 1D and 2D modes. It is a postprocessing technique, since the first stage is the standard radar imaging with the 2D Fourier transform. In addition, selection of the adaptive parameter in this technique is efficient and can be performed based on simple rules in real time. The ...

Fractional Fourier transform (FRFT) performs a rotation of signals in the time—frequency plane, and it has many theories and applications in time-varying signal analysis. Because of the importance of fractional Fourier transform, the implementation of discrete fractional Fourier transform will be an important issue. Recently, a discrete fractional Fourier transform (DFRFT) with discrete Hermite...