Abstract—Frequency transformation with Pascal matrix equations is a method for transforming an electronic filter (analogue or digital) into another filter. The technique is based on frequency transformation in the s-domain, bilinear z-transform with pre-warping frequency, inverse bilinear transformation and a very useful application of the Pascal’s triangle that simplifies computing and enables...

Background: The construction of measurement matrix becomes a focus in compressed sensing (CS) theory. Although random matrices have been theoretically and practically shown to reconstruct signals, it is still necessary to study the more promising deterministic measurement matrix. Methods: In this paper, a new method to construct a simple and efficient deterministic measurement matrix, sparse kr...

Riordan arrays are useful for solving the combinatorial sums by the help of generating functions. Many theorems can be easily proved by Riordan arrays. In this paper we consider the Pascal matrix and define a new generalization of Fibonacci polynomials called p, q -Fibonacci polynomials. We obtain combinatorial identities and by using Riordanmethodwe get factorizations of Pascal matrix involvin...

Recently the author proposed two extensions of Pascal and q-Pascal matrices defined here also in the spirit of the Ward ”Calculus of sequences” [1] promoted in the framework of the ψFinite Operator Calculus [2,3] . Specifications to q-calculus case and Fibonomial calculus case are made explicit as an example of abundance of new possibilities being opened. In broader context the ψ-Pascal Pψ[x] a...

Two matrix equations, Pascal matrix equation and inverse Pascal matrix, are derived and demonstrated in this work. These matrix equations are used for making a conversion and inversion between the coefficients of an analog low pass filter transfer function H(s) and a digital transfer function H(z). The involving of the Pascal’s triangle in both matrix equations is helpful, easier to transform b...