Journal ArticleDOI
The discrete Pascal transform and its applications
Maurice F. Aburdene,T.J. Goodman +1 more
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A new discrete polynomial transform constructed from the rows of Pascal's triangle is introduced, and applications of the transform in digital image processing, such as bump and edge detection are discussed.Abstract:
We introduce a new discrete polynomial transform constructed from the rows of Pascal's triangle. The forward and inverse transforms are computed the same way in both the one- and two-dimensional cases, and the transform matrix can be factored into binary matrices for efficient hardware implementation. We conclude by discussing applications of the transform in digital image processing, such as bump and edge detection.read more
Citations
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Proceedings ArticleDOI
Passive sensing for adaptable radar bandwidth
TL;DR: It will be shown that the proposed technique identifies frequency sub-bands of high SINR while maintaining range resolution requirements, and a spectrum sensing experiment is conducted to collect multiple frequency spectra that are processed by the technique.
Journal ArticleDOI
Fast discrete Pascal transform
TL;DR: An efficient structure for the fast computation of the discrete Pascal transform (DPT) is presented, where only ½N(N−1) additions are required for the computation of an N-point DPT.
Journal ArticleDOI
Low-Complexity and High-Modularity Structure for Implementing Transient-Free Pascal-Delay Filter
TL;DR: An efficient structure for the low-complexity and high-modularity implementation of this Pascal-type VD filter that greatly reduces the multiplication operations required in the filtering process and can achieve more accurate signal-interpolation results than other structures that have the transient problem.
Journal ArticleDOI
Adaptable bandwidth for harmonic step-frequency radar
Anthony F. Martone,Kyle A. Gallagher,Kelly D. Sherbondy,Kenneth I. Ranney,Traian Dogaru,Gregory J. Mazzaro,Ram M. Narayanan +6 more
TL;DR: In this article, a spectrum sensing technique is proposed to enhance the performance of harmonic step-frequency radar in the presence of harmful radio frequency (RF) interference (RFI) interference.
Proceedings ArticleDOI
On the use of the discrete Pascal transform in hiding data in images
TL;DR: Comparisons with existing methods prove the superiority of the proposed method for secretly embedding messages into color images, which is based on dividing each color image component into even-sized blocks.
References
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Journal ArticleDOI
Inverse Relations and Combinatorial Identities
TL;DR: Inverse Relations and Combinatorial Identities: Inverse relations and combinatorial identities as mentioned in this paper are a generalization of the notion of Inverse Relations in algebraic geometry.
Journal ArticleDOI
The bilinear Z transform by Pascal matrix and its application in the design of digital filters
TL;DR: The inverse Pascal matrix can be obtained without computing the determinant of the system, and then it is very easy to obtain the associated analog transfer function H(s) if the discrete transfer functions H(z) is known.
Journal ArticleDOI
Information retrieval in digital watermarking
TL;DR: This work investigates how to design good watermark detectors taking into account the basics of communication theory and discusses different ways to achieve robustness to geometrical attacks and elaborate on watermark attacks.
Journal ArticleDOI
z transform from lowpass to bandpass by Pascal matrix
TL;DR: The inverse Pascal matrix can be obtained without computing the determinant; therefore, if the H(z) is known, then the associated analog transfer function H(s) is very easy to obtain.
Journal ArticleDOI
Unification of Legendre, Laguerre, Hermite, and binomial discrete transforms using Pascal's matrix
TL;DR: The fundamental finding is based on the discovery of the relationship between Pascal's matrix and the binomial coefficient.