In a two-dimensional pattern matching problem, a known template image has be located in another image, irrespective of the template's position, orientation and size in the image. One way to accomplish invariance to the changes in the template is by forming a set of feature vectors that encompass all the variations in the template. Matching is then performed by finding the best similarity betwee...

In this paper, a signal processing framework in a generalized Fourier domain (GFD) is introduced. In this newly proposed domain, a parametric form of control on the periodic repetitions that occur due to sampling in the reciprocal domain is possible, without the need to increase the sampling rate. This characteristic and the connections of the generalized Fourier transform to analyticity and to...

Our aim in this paper is to prove an analog of Younis's Theorem on the image under the Jacobi transform of a class functions satisfying a generalized Dini-Lipschitz condition in the space $mathrm{L}_{(alpha,beta)}^{p}(mathbb{R}^{+})$, $(1< pleq 2)$. It is a version of Titchmarsh's theorem on the description of the image under the Fourier transform of a class of functions satisfying the Dini-Lip...

AA-LP Anti-aliasing lowpass AC3 Adaptive transform coder 3 ACR Absolute-category rating ADC Analog-to-digital converter ADPCM Adaptive differential pulse-code modulation AEC Acoustic echo cancellation / caneller AIR Acoustic impulse response ALP Adaptive lattice predictor ANC Active noise control or adaptive noise canceller AP Affine projection APC Adaptive predictive coding AR Auto-regressive ...

The linear canonical transform (LCT) is the name of a parameterized continuum of transforms that include, as particular cases, many widely used transforms in optics such as the Fourier transform, fractional Fourier transform, and Fresnel transform. It provides a generalized mathematical tool for representing the response of any first-order optical system in a simple and insightful way. In this ...

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...

The linear transform kernel for fractional Fourier transforms is derived. The spatial resolution and the space-bandwidth product for propagation in graded-index media are discussed in direct relation to fractional Fourier transforms, and numerical examples are presented. It is shown how fractional Fourier transforms can be made the basis of generalized spatial filtering systems: Several filters...