The fractional Fourier transform is a natural generalization of the transform. In this work, we recall definition and its relation to conventional We exhibit that permits one obtain easily main properties investigate sharp Hausdorff-Young inequality for utilize it build Matolcsi-Szücs related other versions inequalities concerning also discussed in detail. results obtained paper are very signif...

The fractional Fourier transforms (FrFTs) is one-parametric family of unitary transformations {F} α=0. FrFTs found a lot of applications in signal and image processing. The identical and classical Fourier transformations are both the special cases of the FrFTs. They correspond to α = 0 (F = I) and α = π/2 (F = F), respectively. Up to now, the fractional Fourier spectra Fi = Fi {f} , i = 1, 2, ....

The fractional Fourier transform is a new concept in the theory of time-frequency representations. Closely linked to the Wigner distribution through the Radon transform, it introduces frequency-time hybrid domains in which the signal and the noise could be interwoven differently than in either the time or the frequency domain. The fractional transform breaks down a signal into elementary chirp ...

Various transforms are employed for signal processing to obtain useful information, which is not explicitly available when the signal is in the time domain. Most of the real time signals such as speech, biomedical signals, etc., are non-stationary signals. The Fourier transform (FT), used for most of the signal processing applications, determines the frequency components present in the signal b...

Several signal processing tools are integrated into machine learning models for performance and computational cost improvements. Fourier transform (FT) its variants, which powerful spectral analysis, employed in the prediction of univariate time series by converting them to sequences domain be processed further recurrent neural networks (RNNs). This approach increases reduces training compared ...

The paper examines the Fractional Fourier Transform (FRFT) based technique as a tool for obtaining probability density function and its derivatives, mainly fitting stochastic model with fundamental probabilistic relationships of infinite divisibility. functions are computed, distributional proprieties reviewed Variance-Gamma (VG) model. VG has been increasingly used an alternative to Classical ...

Certain solutions to Harper’s equation are discrete analogues of (and approximations to) the Hermite–Gaussian functions. They are the energy eigenfunctions of a discrete algebraic analogue of the harmonic oscillator, and they lead to a definition of a discrete fractional Fourier transform (FT). The discrete fractional FT is essentially the time-evolution operator of the discrete harmonic oscill...

The fractional cosine and sine transforms – closely related to the fractional Fourier transform, which is now actively used in optics and signal processing, and to the fractional Hartley transform – are introduced and their main properties and possible applications as elementary fractional transforms of causal signals are discussed.

In digital watermarking, a watermark is embedded into a cover image in such a way that the resulting watermarked signal is robust to certain distortion caused by either standard data processing in a friendly environment or malicious attacks in an unfriendly environment. This work provides Digital image watermarking based on Fractional Fourier transform and two dimensional fast Fourier transform...

The linear canonical transform(LCT) has become a very active area in signal processing community in recent years, with many applications in optics, radar system analysis, filter design, phase retrieval, pattern recognition, etc. Many well-known transforms such as the Fourier transform,the fractional Fourier transform,and the Fresnel transform can be seen as special cases of the linear canonical...