Discrete Pseudo-Fractional Fourier Transform and Its Fast Algorithm

In this article, we introduce a new discrete fractional transform for data sequences whose size is a composite number. The main kernels of the introduced transform are small-size discrete fractional Fourier transforms. Since the introduced transformation is not, in the generally known sense, a classical discrete fractional transform, we call it discrete pseudo-fractional Fourier transform. We also provide a generalization of this new transform, which depends on many fractional parameters. A fast algorithm for computing the introduced transform is developed and described.

AN ITERATIVE ALGORITHM FOR NONLINEAR FRACTIONAL-ORDER OSCILLATORS WITH MODIFIED RIEMANN-LIOUVILLE DERIVATIVE

This paper presents an iterative analytic algorithm for the approximate solution of nonlinear fractional-order oscillators. He fractional transform was applied to convert the fractional-order model, defined by a modified Riemann-Liouville derivative, to a model in continuous spacetime. Then, the approximate solution of the continuous model was applied to obtain an approximate solution for the fractional-order oscillator. The solution was obtained using the continuous piecewise linearization method (CPLM), which is a simple, accurate and efficient analytic algorithm. The applicability of the CPLM was demonstrated using representative examples in science and engineering and the maximum relative error of the approximate solution was found to be less than 0.2%. This paper provides an analytical tool that can be applied in the study of fractional-order oscillations arising in various physical systems and technological processes.

Video Coding of Various Decomposition with Encoding Techniques

In a period of past ten years, Compression or coding of video has been elaborated as a vital role in the part of total communication. Multi resolutions techniques play a vital part in the coding of image and video. Wavelet and curve let transform are one of the popular and efficient technique in video coding. In my paper, I am operate to implement various coding based methods with (EWT)empirical wavelet transform, different wavelets ,curvelets with various encoding techniques. They are video coding with EWT and H.264(VEWH), video coding with EWT and LZW(VEWL), video coding with EWT and Huffman with SPIHT(VEWHS), video coding with mexican hat wavelet transform and SPIHT(VMWS), video coding with dual tree wavelet and SPIHT(VDTS), video coding with 3D dual tree wavelet transform and SPIHT(V3DTS), video coding with curvelet transform and SPIHT(VCTS) and video coding with dual tree complex wavelet fractional transform and modified SPIHT(VDTCWFS). Next we implement these methods with the assist of matlab 2014 and 2015, and then analyze these techniques by using PSNR and compression ratio