The performance of Orthogonal Frequency Division Multiple Access (OFDMA) system degrades significantly in doubly dispersive channels. This is due to the fact that exponential sub-carriers do not match the singular functions of this type of channels. To solve this problem, we develop a system whose sub-carriers are chirp functions. This is equivalent to exploiting FRACTIONAL FOURIER TRANSFORM (FrFT) instead of FOURIER TRANSFORM (FT) in the structure of the aforementioned transmission scheme. We name the new system FrFT-OFDMA. The optimal angle of FRACTIONAL FOURIER TRANSFORM for each user depends on its channel parameters. Thus, the angles of TRANSFORM for different users are not necessarily identical. This destroys the orthogonality of users and generates Multi-User Interference (MUI). By analyzing MUI, we introduce quasi-orthogonality conditions where interference is negligible despite different angles of TRANSFORM. For non-orthogonal users, we propose a method to mitigate MUI. We present the efficiency of this method through comparative performance evaluation of the conventional system based on FT and the new system based on FrFT. We show that our proposed transmission scheme outperforms the traditional OFDMA system significantly in doubly dispersive channels and channels impaired by frequency offset.

Changes in earth surface features may occur due to internal or external changes.  However, regardless of the origin of the change, detection and monitoring of these changes will contribute to environmental planning for sustainable development and optimal utilization of resources. In this sense, introducing and implementing methods that are successful in recognizing the magnitude and trend of change will be useful. For this reason, the processing of satellite images in different sciences and with different purposes has become one of the main areas of research. This study aims to identify the changing areas frequency domain using discrete FRACTIONAL FOURIER TRANSFORM method and the optimal order of discrete FRACTIONAL FOURIER TRANSFORM to determine the accuracy and completeness of change detection in satellite images. In this regard, due to the inability of existing software packages on detecting changes using discrete FOURIER TRANSFORM, a software has been developed in MATLAB environment. First, the accuracy of the output generated through developed software was evaluated on differential sample images. Then, using Landsat and Sentinel2 satellite images from different dates and finding the value of coefficient “a” in the FOURIER fraction TRANSFORM, different outputs were obtained. Here, the results of the change image obtained from the optimal FRACTIONAL FOURIER TRANSFORM method were compared with the difference image.  The bands 2, 3 and 4 of Sentinel 2 did not indicate any sensitivity to changes in geological structures. However, they showed most of the changes in vegetated areas.  However, band 8 (infrared band) of this sensor not only detected changes on vegetated areas, but also revealed changes in geological structures.

Introduction: Clinical performance of light cured resin composites is related to their degree of polymerization. The purpose of this study was to compare the degree of conversion of packable and hybrid composites by FTIR (FOURIER TRANSFORM Infrared Spectroscopy).Materials & Methods: In this experimental study, 40 composite disks were prepared in two groups from Z250 and P60 composites. Each group was divided into four subgroups (2mm thickness cured with QTH unit, 2mm thickness cured with LED unit, 5mm thickness cured with QTH unit, and 5mm thickness cured with LED unit). Then samples were evaluated by FTIR to determine the degree of conversion (DC). Data were analyzed by Kolmogorov-Smirnov and three way ANOVA.Results: There was not a significant difference among the DC of the materials tested. LED significantly increased the degree of conversion of materials tested (P<0.001). DC values were significantly greater in 2mm diameter samples vs 5mm ones (P<0.001).Conclusion: The use of incremental technique in deep cavities restored with these composites is suggested. Also using LED is advised for curing composites because of a better result.

In this manuscript, we review fractal calculus and the analogues of both local FOURIER TRANSFORM with its related properties and FOURIER convolution theorem are proposed with proofs in fractal calculus. The fractal Dirac delta with its derivative and the fractal FOURIER TRANSFORM of the Dirac delta is also defined. In addition, some important applications of the local fractal FOURIER TRANSFORM are presented in this paper such as the fractal electric current in a simple circuit, the fractal second order ordinary differential equation, and the fractal Bernoulli-Euler beam equation. All discussed applications are closely related to the fact that, in fractal calculus, a useful local fractal derivative is a generalized local derivative in the standard calculus sense. In addition, a comparative analysis is also carried out to explain the benefits of this fractal calculus parameter on the basis of the additional alpha parameter, which is the dimension of the fractal set, such that when α,= 1, we obtain the same results in the standard calculus.

One of the main challenges in speech recognition is noise resistant feature extraction. In this paper, a new feature extraction algorithm, called FRACTIONAL and Adaptive Power Normalized Cepstral Coefficients Algorithm, has been proposed as a noise-resistant method for speech recognition. This proposed feature extraction method is based on a FRACTIONAL short-term FOURIER TRANSFORM. The selection of FRACTIONAL conversion coefficient is important for proper analysis of multi-component signals like speech. Therefore, the proposed method obtains the optimum parameter of α for FRACTIONAL FOURIER TRANSFORM based on the noise class in the environment, adaptively by the Differential Evolution meta-heuristic algorithm. Moreover, TI Digit and Noisex-92 are used for evaluation of the resistance and accuracy of the recognition of the automatic speech recognition system. Simulation results show more resistance and higher recognition accuracy of the proposed feature extraction method rather than other methods in noisy and without noise environments. In the proposed ASR system, the Support Vector Machine (SVM) classifier with a nonlinear kernel has been used. Also, all the simulations are performed in MATLAB.

Digital holographic Microscopy is a non-destructive and label-free method that provides quantitative phase information in biological and industrial applications. High coherence light sources, such as lasers, are commonly used in digital holographic microscopes. Parasitic -interference fringes and speckle noise in high-coherence sources as well as complex configurations reduce the accuracy of the phase measurements. In this paper, a common-path and low-coherence digital holographic microscopy with a FOURIER TRANSFORM-based spectroscopy is introduced. The low-coherence source used here is an LED and the common path configuration is used based on splitting the wavefront by Fresnel biprism. Reconstruction of the hologram is analyzed using the FOURIER method. In addition, The spectral line shape of the LED is obtained simultaneously with the FOURIER TRANSFORM of the visibility of the recorded fringes. The ability to simultaneously perform quantitative phase imaging and FOURIER TRANSFORM spectroscopy makes this system unique in the real-time study of biological samples in micron size.