Browsing by Subject "Quadratic phase function"

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Open Access
Laplace transforms of a family of functions related to quadratic phase function
(IEEE, 2022-07-08) Onural, Levent
A parametric family of complex valued functions in the form of quadratic exponents are defined starting from the real valued Gaussian function. The family of functions include the quadratic phase function, which is also called the two-sided complex chirp. It is proven using contour integrals on the complex plane that the Laplace transforms of these functions are also complex valued quadratic exponents; the region of convergence of the Laplace transform include the entire s -plane for finite |s| for a range of values of the defining parameter of the family. Fourier transforms are also presented as the special cases of the Laplace transform.
Open Access
Some mathematical properties of the uniformly sampled quadratic phase function and associated issues in digital Fresnel diffraction simulations
(SPIE - International Society for Optical Engineering, 2004) Onural, L.
The quadratic phase function is fundamental in describing and computing wave-propagation-related phenomena under the Fresnel approximation; it is also frequently used in many signal processing algorithms. This function has interesting properties and Fourier transform relations. For example, the Fourier transform of the sampled chirp is also a sampled chirp for some sampling rates. These properties are essential in interpreting the aliasing and its effects as a consequence of sampling of the quadratic phase function, and lead to interesting and efficient algorithms to simulate Fresnel diffraction. For example, it is possible to construct discrete Fourier transform (DFT)-based algorithms to compute exact continuous Fresnel diffraction patterns of continuous, not necessarily, periodic masks at some specific distances. © 2004 Society of Photo-Optical Instrumentation Engineers.