Hartley transform

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

Zak transform and uncertainty principles associated with the linear canonical transform

Abstract: Several new results about Zak transform and uncertainty principles in the linear canonical transform (LCT) domains are presented. The results obtained rely mainly on relationship between the LCT and the classical Fourier transform. The findings will likely have potential applications in optics and signal processing.

Iterative approximation environments for modeling the evolution of an image propagating through a physical medium in restoration and other applications

Abstract: Image processing utilizing numerical calculation of fractional exponential powers of a diagonalizable numerical transform operator for use in an iterative or other larger computational environments. In one implementation, a computation involving a similarity transformation is partitioned so that one part remains fixed and may be reused in subsequent iterations. The numerical transform operator may be a discrete Fourier transform operator, discrete fractional Fourier transform operator, centered discrete fractional Fourier transform operator, and other operators, modeling propagation through physical media. Such iterative environments for these types of numerical calculations are useful in correcting the focus of misfocused images which may originate from optical processes involving light (for example, with a lens or lens system) or from particle beams (for example, in electron microscopy or ion lithography).

Numerical evaluation of the Hilbert transform by the Fast Fourier Transform (FFT) technique

Abstract: Summary. Three Fast Fourier Transform numerical methods for computing the Hilbert transform have been evaluated for their accuracy by numerical examples. All three methods employ the property that the Hdbert transform is a convolution. The first method uses the result that the Fourier transform of 1/πx is — isgn(ω). The second method is based on a discrete Hilbert transform introduced by Saito. The third method, introduced in this research note, uses linear interpolation to transform the Hilbert transform integral into a discrete convolution. The last method is shown by numerical examples from fault dislocation models to be more accurate than the other two methods when the Hilbert transform integral has high-frequency components.

Improved implementation algorithms of the two-dimensional nonseparable linear canonical transform.

Abstract: The two-dimensional nonseparable linear canonical transform (2D NSLCT), which is a generalization of the fractional Fourier transform and the linear canonical transform, is useful for analyzing optical systems. However, since the 2D NSLCT has 16 parameters and is very complicated, it is a great challenge to implement it in an efficient way. In this paper, we improved the previous work and propose an efficient way to implement the 2D NSLCT. The proposed algorithm can minimize the numerical error arising from interpolation operations and requires fewer chirp multiplications. The simulation results show that, compared with the existing algorithm, the proposed algorithms can implement the 2D NSLCT more accurately and the required computation time is also less.

New fast algorithm to compute two-dimensional discrete Hartley transform

Abstract: A new fast algorithm for computing the two-dimensional discrete Hartley transform is presented. This algorithm requires the lowest number of multiplications compared with other related algorithms.