*Correspondence: Hatsuo Ishida, Department of Macromolecular Science and Engineering, Case Western Reserve University, Cleveland, OH 44106, USA e-mail: [email protected] High-performance thermosets via amide–imide functional benzoxazine resins as precursors have been synthesized.The structures of synthesized monomers have been confirmed by 1H NMR and Fourier transform infrared. Among these two benz...

In this paper we devise a so-called cylindrical Fourier transform within the Clifford analysis context. The idea is the following: for a fixed vector in the image space the level surfaces of the traditional Fourier kernel are planes perpendicular to that fixed vector. For this Fourier kernel we now substitute a new Clifford-Fourier kernel such that, again for a fixed vector in the image space, ...

Nowadays, Radar systems have many applications and radar imaging is one of the most important of these applications. Inverse Synthetic Aperture Radar (ISAR) is used to form an image from moving targets. Conventional methods use Fourier transform to retrieve Doppler information. However, because of maneuvering of the target, the Doppler spectrum becomes time-varying and the image is blurred. Joi...

In X-ray tomography, the Fourier slice theorem provides a relationship between the Fourier components of the object being imaged and the measured projection data. The Fourier slice theorem is the basis for X-ray Fourier-based tomographic inversion techniques. A similar relationship, referred to as the 'Fourier shell identity' has been previously derived for photoacoustic applications. However, ...

By using a spectral approach, we derive a Gaussian-like quadrature of the continuous fractional Fourier transform. The quadrature is obtained from a bilinear form of eigenvectors of the matrix associated to the recurrence equation of the Hermite polynomials. These eigenvectors are discrete approximations of the Hermite functions, which are eigenfunctions of the fractional Fourier transform oper...

PURPOSE The purpose of this paper is to implement a noise-weighted filtered backprojection (FBP) algorithm in the form of "convolution" backprojection, but this "convolution" has a spatially variant integration kernel. METHODS Noise-weighted FBP algorithms have been developed in recent years, with filtering being performed in the Fourier domain. The noise weighting makes the ramp filter in th...