Topic
Fractional Fourier transform
About: Fractional Fourier transform is a research topic. Over the lifetime, 9263 publications have been published within this topic receiving 224088 citations.
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30 Jun 2022TL;DR: In this paper , the quadratic phase Fourier transform (QPFT) was generalized to quaternion valued signals, known as the Quaternion QPFT (QPT) QPT, and the inverse transform and Parseval and Plancherel formulas associated with it were derived.
Abstract: The quadratic phase Fourier transform QPFT is a neoteric addition to the class of Fourier transforms and embodies a variety of signal processing tools including the Fourier, fractional Fourier, linear canonical, and special affine Fourier transform. In this paper, we generalize the quadratic phase Fourier transform to quaternion valued signals, known as the quaternion QPFT QQPFT. We initiate our investigation by studying the QPFT of 2D quaternionic signals, then we introduce the QQPFT of 2D quaternionic signals. Using the fundamental relationship between the QQPFT and quaternion Fourier transform QFT, we derive the inverse transform and Parseval and Plancherel formulas associated with the QQPFT. Some other properties including linearity, shift and modulation of the QQPFT are also studied. Finally, we formulate several classes of uncertainty principles UPs for the QQPFT, which including Heisenberg type UP, logarithmic UP, Hardys UP, Beurlings UP and Donohon Starks UP. It can be regarded as the first step in the applications of the QQPFT in the real world.
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TL;DR: In this article, an algorithm for the selection and assignment of the parameter a of a numerical inversion of a Laplace transform with the use of Fourier series is presented, where the parameter is chosen based on the Fourier coefficients.
Abstract: An algorithm is examined for the selection and assignment of the parameter a of a numerical inversion of a Laplace transform with the use of Fourier series.
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TL;DR: In this article, the authors extended the results of fractional Fourier transform to integrable Boehmians given by Zayed (12) and proved the properties of the result.
Abstract: In this paper we have extended the results of fractional Fourier transform to integrable Boehmians given by Zayed (12) and prove its properties. Further, an inversion theorem of the same is established.
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05 May 2020
TL;DR: In this article, the authors used Linear Canonical Transform (LCT) for the encryption process, which can be used to improve the robustness and imperceptibility of non-stationary images.
Abstract: Data security is a prime objective of various researchers & organizations. Because we have to send the data from one end to another end so it is very much important for the sender that the information will reach to the authorized receiver & with minimum loss in the original data. Data security is required in various fields like banking, defence, medical etc. So our objective here is that how to secure the data. So for this purpose we have to use encryption schemes. Encryption is basically used to secure the data or information which we have to transmit or to store. Various methods for the encryption are provided by various researchers. Some of the methods are based on the random keys & some are based on the scrambling scheme. Chaotic map, logistic map, Fourier transform & Fractional Fourier transform etc. are widely used for the encryption process. Now day’s image encryption method is very popular for the encryption scheme. The information is encrypted in the form of image. The encryption is done in a format so no one can read that image. Only the person who are authenticated or have authentication keys can only read that data or information. So this work is based on the same fundamental concept. Here we use Linear Canonical Transform for the encryption process. Data encryption technology is used to benefit protection against loss, exploitation or afilteration of private information. As a result of this approach for the validation Mean Square Error (MSE) & Correlation Coefficients (CC) measured. Robustness & imperceptibility of non-stationary images can be improved by using the proposed technique.
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06 Feb 2011
TL;DR: This paper presents a method for speeding-up computing the traces by using decision diagrams to operate on matrix-valued group representations and related Fourier coefficients.
Abstract: The Fourier transform is a classical method in mathematical modeling of systems. Assuming finite non-Abelian groups as the underlying mathematical structure might bring advantages in modeling certain systems often met in computer science and information technologies. Frequent computing of the inverse Fourier transform is usually required in dealing with such systems. These computations require for each function value to compute many times traces of certain matrices. These matrices are products of matrix-valued entries of unitary irreducible representations and matrix-valued Fourier coefficients. In the case of large non-Abelian groups the complexity of these computations can be a limiting factor in applications. In this paper, we present a method for speeding-up computing the traces by using decision diagrams to operate on matrix-valued group representations and related Fourier coefficients.