Conventional Fourier analysis has many schemes for different types of signals. They are Fourier transform (FT), Fourier series (FS), discrete-time Fourier transform (DTFT), and discrete Fourier transform (DFT). The goal of this correspondence is to develop two absent schemes of fractional Fourier analysis methods. The proposed methods are fractional Fourier series (FRFS) and discrete-time fract...

Joint Fourier transform correlation is an analog optical signal processing technique capable of comparing several two-dimensional images. We show that selected spectral domain binary thresholds, obtained through simulation, signiicantly improve the performance of an optical implementation of the joint transform correlator. In doing so we establish empirically the existence of well deened optima...

The spectral analysis of uniform or nonuniform sampling signal is one of the hot topics in digital signal processing community. Theories and applications of uniformly and nonuniformly sampled one-dimensional or two-dimensional signals in the traditional Fourier domain have been well studied. But so far, none of the research papers focusing on the spectral analysis of sampled signals in the line...

Efficient representation of images usually leads to improvements in storage efficiency, computational complexity and performance of image processing algorithms. Efficient representation of images can be achieved by transforms. However, conventional transforms such as Fourier transform and wavelet transform suffer from discontinuities such as edges in images. To address this problem, we propose ...

A new image denoising method based on curvelet transform is proposed. The limitations of commonly used separable extensions of one-dimensional transforms, such as the Fourier and wavelet transforms, in capturing the geometry of image edges are well known. Here, we pursue "true" two-dimensional transform that can capture the intrinsic geometrical structure that is key in visual information. Deno...

The windowed Fourier transform of a time signal is considered, as well as a way to reconstruct the signal from a su ciently densely sampled version of its windowed Fourier transform using a Gabor representation; followingGabor, sampling occurs on a two-dimensional time-frequency lattice with equidistant time intervals and equidistant frequency intervals. In the limit of innitely dense sampling,...

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...