The pseudo-polar Fourier transform is a specialized non-equally spaced Fourier transform, which evaluates the Fourier transform on a near-polar grid, known as the pseudo-polar grid. The advantage of the pseudo-polar grid over other non-uniform sampling geometries is that the transformation, which samples the Fourier transform on the pseudo-polar grid, can be inverted using a fast and stable alg...

The pseudo-polar Fourier transform is a specialized nonequally spaced Fourier transform, which evaluates the Fourier transform on a near-polar grid known as the pseudo-polar grid. The advantage of the pseudo-polar grid over other nonuniform sampling geometries is that the transformation, which samples the Fourier transform on the pseudo-polar grid, can be inverted using a fast and stable algori...

The general goal of this paper is to extend the parallel-beam projection-slice theorem to divergent fan-beam and cone-beam projections without rebinning the divergent fan-beam and cone-beam projections into parallel-beam projections directly. The basic idea is to establish a novel link between the local Fourier transform of the projection data and the Fourier transform of the image object. Anal...

7 Trigonometric Identities, Complex Exponentials and Periodic Sequences 26 7.1 Basic Trigonometric Identities . . . . . . . . . . . . . . . . . . 26 7.2 Basic Trigonometric Integrals . . . . . . . . . . . . . . . . . . 28 7.3 Basic Properties of Complex Numbers . . . . . . . . . . . . . 29 7.4 Complex Numbers and Trigonometrical Identities . . . . . . . 31 7.5 The Exponential of a Complex Numbe...

This paper is focused on the problem of mode identification of Lamb waves in ultrasonic testing, and the principle and process of two time-frequency transform method, smooth pseudo Wigner–Ville distribution and two-dimensional Fourier transform, were discussed. The experimental work were carried out in aluminium plates, and the single and multimode Lamb waves were excited by 5MHz oblique incide...

In this paper, a comparison between three different filters in the 3D scanning processes by Fourier Transform two-dimensional. The implementation and comparison about the filter by threshold, morphological filtering like rectangle and elliptic, the representation about the filters are in a binary mask and it is multiplied by the spectrum of Fourier Transform two-dimensional, with this process t...

The Fourier transform proves indispensable in the processing of classical information as well quantum domain, where it finds many applications ranging from state reconstruction to prime factoring. An implementation scheme $d$-dimensional acting on single photons is known that uses path encoding and requires $O(d \log d)$ optical elements. In this paper we present an alternative design orbital a...