Hartley transform

About: Hartley transform is a research topic. Over the lifetime, 2709 publications have been published within this topic receiving 79944 citations.

A discretization of the continuous fourier transform

Abstract: A finite representation of the continuous Fourier transform is obtained in a linear space of dimensionN for the Hermite functions by using some properties of the Hermite polynomialsHN(x) and its zeros. TheN-dimensional vectors representing a Hermite function and its Fourier-trnasformed function converge to their exact continuous values whenN→∞. The genericN×N matrix representing the kernel of the continuous transform exp [−ipx], preserves the conspicuous properties of this function, and their entries approach the values that this kernel takes atp=xj andx=xk, wherexj andxk are two zeros ofHN(x) whenN→∞. These properties lead to propose this kind of matrices as finite representations of the kernel of the continuous Fourier transform for functions other than the Hermite ones, yielding certain quadrature formula for this transform. Some numerical examples of this application are shown and they are compared with those obtained through standard procedures.

Fractional wave packet transform

Abstract: The short-time Fourier transform (STFT), or windowed Fourier transform, is the most widely used method in signal processing. We introduce the concept of the fractional wave packet transform (FRWPT), based on the idea of the fractional Fourier transform (FRFT) and wave packet transform (WPT). We show a version of the resolution of the identity and some properties of FRWPT connected with those of the FRFT and WPT.

Asymmetric encryption algorithm for colour images based on fractional Hartley transform

Abstract: This paper presents a new scheme for encryption of single-channel colour images. The scheme uses amplitude- and phase-truncation approach to introduce non-linearity for enhanced security. Further, the colour image encryption is performed in the fractional Hartley domain, which is relatively less investigated. The encryption starts with an affine transform of each channel of the input colour image. Thereafter, one of the channels is considered as the input amplitude image while the other two are used as phase masks, one in the spatial and the other in the frequency domain. A detailed analysis of the scheme’s sensitivity to various encryption parameters has been carried out. In addition, security analysis of the scheme against attacks establishes the scheme’s robustness. The combined use of the affine transform and phase-truncation approach for colour image encryption in the fractional Hartley domain is attempted for the first time in this study. It is shown that the proposed scheme resists the spec...

The power spectrum of the Mellin transformation with applications to scaling of physical quantities

Abstract: The Mellin transform is used to diagonalize the dilation operator in a manner analogous to the use of the Fourier transform to diagonalize the translation operator. A power spectrum is also introduced for the Mellin transform which is analogous to that used for the Fourier transform. Unlike the case for the power spectrum of the Fourier transform where sharp peaks correspond to periodicities in translation, the peaks in the power spectrum of the Mellin transform correspond to periodicities in magnification. A theorem of Wiener‐Khinchine type is introduced for the Mellin transform power spectrum. It is expected that the new power spectrum will play an important role extracting meaningful information from noisy data and will thus be a useful complement to the use of the ordinary Fourier power spectrum.