Random sampling can lead to algorithms where the Fourier reconstruction is almost perfect when the underlying spectrum of the signal is sparse or band-limited. Conversely, regular sampling often hampers the Fourier data recovery methods. However, two-dimensional (2D) signals which are band-limited in one spatial dimension can be recovered by designing a regular acquisition grid that minimizes t...

Rotation Due to the rotation property of the two-dimensional Fourier transform rotation of f (x , y) through an angle & also rotates the spectrum by the same amount. It is also well known that the Fourier spectrum (modulus) is invariant to translation. Now, suppose that we scan the Fourier spectrum IF,(along a circle centered at the origin. If circular sampling of 1 F,I * is used, then by takin...

The Lomb-Scargle periodogram is widely used for the estimation of the power spectral density of unevenly sampled data. A small extension of the algorithm of the Lomb-Scargle periodogram permits the estimation of the phases of the spectral components. The amplitude and phase information is sufficient for the construction of a complex Fourier spectrum. The inverse Fourier transform can be applied...

Atomic resolution and coarse-grained simulations of dimyristoylphosphatidylcholine lipid bilayers were analyzed for fluctuations perpendicular to the bilayer using a completely Fourier-based method. We find that the fluctuation spectrum of motions perpendicular to the bilayer can be decomposed into just two parts: 1), a pure undulation spectrum proportional to q(-4) that dominates in the small-...

obtaining a seismic section with high temporal and spatial resolution was always one of the goals of seismic data processors and interpreters. accurate estimation of the thicknesses of thin beds is an important tool in this regard. the basic problem is that the wavelength of the signal must be similar in dimention to that of the bed thinness. if it is much longer than the bed thinness, the dete...

in this research zinc oxide (zno) nano-crystalline powders were prepared by sol-gel method using zinc acetate. the zno nanoparticles were characterized by x-ray diffraction (xrd), scanning electron microscopy (sem), ultraviolet-visible (uv-vis), fourier transform infra-red (ft-ir) and energy dispersive x-ray (edx) spectroscopy. the structure of nanoparticles was studied using xrd pattern. the c...

cadmium oxide (cdo) nanoparticles were prepared by precipitation method using cadmium acetate and ammonia solution. presence of chemical species, were verified by fourier transform infra red (ftir) spectrum. from x-ray diffraction (xrd) spectrum the particle size, d-spacing value and structure of the nanoparticle were analysed. size of the nanoparticles and the elemental composition were detect...

We describe a Fourier Volume Rendering (FVR) algorithm for datasets that are irregularly sampled and require anisotropic (e.g., elliptical) kernels for reconstruction. We sample the continuous frequency spectrum of such datasets by computing the continuous Fourier transform of the spatial interpolation kernel which is a radially symmetric Gaussian basis function (RBF) that may be anisotropicall...