Robust Image Compression Algorithm using Discrete Fractional Cosine Transform

The discrete fractional Fourier transform become paradigm in signal processing. This transform process the signal in joint time-frequency domain. The attractive and very important feature of DFrCT is an availability of extra degree of one free parameter that is provided by fractional orders and due to which optimization is possible. Less execution time and easy implementation are main advantages of proposed algorithm. The merit of effectiveness of proposed technique over existing technique is superior due to application of discrete fractional cosine transform by which higher compression ratio and PSNR are obtained without any artifacts in compressed images. The novelty of the proposed algorithm is no artifacts in compressed image along with good CR and PSNR. Compression ratio (CR) and peak signal to noise ratio (PSNR) are quality parameters for image compression with optimum fractional order.

Multiweighted-Type Fractional Fourier Transform: Unitarity

The definition of the discrete fractional Fourier transform (DFRFT) varies, and the multiweighted-type fractional Fourier transform (M-WFRFT) is its extended definition. It is not easy to prove its unitarity. We use the weighted-type fractional Fourier transform, fractional-order matrix and eigendecomposition-type fractional Fourier transform as basic functions to prove and discuss the unitarity. Thanks to the growing body of research, we found that the effective weighting term of the M-WFRFT is only four terms, none of which are extended to M terms, as described in the definition. Furthermore, the program code is analyzed, and the result shows that the previous work (Digit Signal Process 2020: 104: 18) based on MATLAB for unitary verification is inaccurate.

Some Structures of Parallel VLSI-Oriented Processing Units for Implementation of Small Size Discrete Fractional Fourier Transforms

Discrete orthogonal transforms such as the discrete Fourier transform, discrete cosine transform, discrete Hartley transform, etc., are important tools in numerical analysis, signal processing, and statistical methods. The successful application of transform techniques relies on the existence of efficient fast algorithms for their implementation. A special place in the list of transformations is occupied by the discrete fractional Fourier transform (DFrFT). In this paper, some parallel algorithms and processing unit structures for fast DFrFT implementation are proposed. The approach is based on the resourceful factorization of DFrFT matrices. Some parallel algorithms and processing unit structures for small size DFrFTs such as N = 2, 3, 4, 5, 6, and 7 are presented. In each case, we describe only the most important part of the structures of the processing units, neglecting the description of the auxiliary units and the control circuits.