This paper introduces a new transform known as HARWHT. It results from the Kronecker product of the discrete Hartley transform (DHT) and discrete Walsh-Hadamard transform (WHT). The eigenvectors and eigenvalues of the HARWHT transform matrices are presented using Kronecker product. Then, the results of the eigen decomposition of the transform matrices are used to define discrete fractional HARW...

The Hilbert transform plays an important role in the theory and practice of signal processing. A generalization of the Hilbert transform, the fractional Hilbert transform, was recently proposed, and it presents physical interpretation in the definition. In this paper, we develop the discrete fractional Hilbert transform, and apply the proposed discrete fractional Hilbert transform to the edge d...

In this paper, we present the first 3D discrete curvelet transform. This transform is an extension to the 2D transform described in Candès et al.. The resulting curvelet frame preserves the important properties, such as parabolic scaling, tightness and sparse representation for singularities of codimension one. We describe three different implementations: in-core, out-of-core and MPI-based para...

Disclaimer: These notes are intended to be an accessible introduction to the subject, with no pretense at completeness. In general, you can find more thorough discussions in Oppenheim's book. Please let me know if you find any typos. In this lecture, we discuss the Discrete Fourier Transform (DFT), which is a fourier representation for finite length signals. The main practical importance of thi...

Hadamard transform is an important tool in discrete signal processing. In this paper, we define the discrete fractional Hadamard transform which is a generalized one. The development of discrete fractional Hadamard is based upon the same spirit of discrete fractional Fourier transform.

In this paper we define a discrete analogue of the continuous diffracted projection. we define a discrete diffracted transform (DDT) as a collection of the discrete diffracted projections taken at specific set of angles along specific set of lines. We define ‘discrete diffracted projection’ to be a discrete transform that is similar in its properties to the continuous diffracted projection. We ...

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A discrete version of the Zak transform is defined and used to analyze discrete Weyl–Heisenberg frames, which are nonorthogonal systems in the space of square-summable sequences that, although not necessarily bases, provide representations of square-summable sequences as sums of the frame elements. While the general theory is essentially similar to the continuous case, major differences occur w...