Symmetry is rarely found on cellular surfaces. An exception is the brush border of microvilli, which are essential for the proper function of transport epithelia. In a healthy intestine, they appear densely packed as a 2D-hexagonal lattice. For in vitro testing of intestinal transport the cell line Caco-2 has been established. As reported by electron microscopy, their microvilli arrange primari...

The idea of two-dimensional Fourier transformation was originated by Jeener (1) in 1971, but the very wide significance of his proposal does not seem to have been generally realized until several years later, when several elegant applications were described (2-6). The basic idea is very simple. In modern nmr spectrometers, spectra are normally obtained by Fourier transformation of a transient f...

Introduction Line scan diffusion imaging (LSDI) [1] is a one-dimensional Fourier encoding techniques. The absence of phase encoding provides considerable robustness against motion and immunity to artifacts due to magnetic field inhomogeneities and susceptibility. Parallel imaging has been successfully applied to accelerate 2D and 3D Fourier imaging by reducing phase encoding steps. Here we prop...

This paper describes a method and implementation for eliminating repetitive 2D patterns in images by interactively editing their Fourier spectra. It includes a brief discussion of the basic mathematical prerequisites, in particular, the 2D Discrete Fourier Transform and its relevant properties. Based on this concept, “InSpectral” is an interactive software application that provides intuitive an...

The publication of the Cooley-Tukey fast Fourier transform (FIT) algorithm in 1965 has opened a new area in digital signal processing by reducing the order of complexity of some crucial computational tasks like Fourier transform and convolution from N 2 to N log2 N, where N is the problem size. The development of the major algorithms (Cooley-Tukey and split-radix FFT, prime factor algorithm and...

The established methodologies for studying computational complexity can be applied to the new problems posed by very large-scale integrated (VLSI) circuits. This thesis develops a “VLsI model of computation” and derives upper and lower bounds on the silicon area and time required to solve the problems of sorting and discrete Fourier transformation. In particular, the area A and time T taken by ...

We present a new algorithm for the 2D Radix-2 Sliding Window Fourier Transform (SWFT). Our algorithm avoids repeating calculations in overlappingwindows by using a tree representation of the Cooley-Tukey Fast Fourier Transform (FFT). For an N0 × N1 array and n0 = 2m0 × n1 = 2m1 windows, our algorithm takes O(N0N1n0n1) operations, which is faster than taking a 2D FFT in each window. We provide a...

We propose a new method called incremental Fourier synthesis to generate 2-D self-similar images based on a 2D fractional Brownian motion (fBm) model. With this method, the stationary increments of fBm are created by a Fourier synthesis method and the increments are added up to generate the nonstationary 2D fBm process. Since the new method takes advantage of the FFT, its computational complexi...

In this paper, we present a comparative study between the modified variational iteration method (MVIM) and a hybrid of Fourier transform and variational iteration method (FTVIM). The study outlines the efficiencyand convergence of the two methods. The analysis is illustrated by investigating four singular partial differential equations with variable coefficients. The solution of singular partia...

Amplified dispersive Fourier transformation (ADFT) is a powerful tool for fast real-time spectroscopy as it overcomes the limitations of traditional optical spectrometers. ADFT maps the spectrum of an optical pulse into a temporal waveform using group-velocity dispersion and simultaneously amplifies it in the optical domain. It greatly simplifies spectroscopy by replacing the diffraction gratin...