In this note we introduce a new family of wavelets, named Chebyshev wavelets, which are derived from conventional Chebyshev polynomials. Properties of Chebyshev filter banks are investigated, including orthogonality and perfect reconstruction conditions. Chebyshev wavelets of 2nd kind have compact support, their filters possess good selectivity, but they are not orthogonal. The convergence into 2nd kind Chebyshev wavelets via the cascade algorithm is proved by the use of Markov chains theorems. Computational implementation of these wavelets and some clear-cut applications are presented. These wavelets are offered as a choice in wavelet analysis.
The knowledge about the true nature of the traffic in computer networking is a key requirement in the design of such networks. The phenomenon of self-similarity is a characteristic of the traffic of current client/server packet networks in LAN/ environments dominated by network technologies such as Ethernet and the TCP/IP protocol stack. The development of networks traffic simulators, which take into account this attribute, is necessary for a more realistic description the traffic on these networks and their use in the design of resources (contention elements) and protocols of flow control and network congestion. In this scenario it is recommended do not adopt standard traffic models of the Poisson type.
Finite field transforms have many applications and, in many cases, can be implemented with a low computational complexity. In this paper, the Z Transform over a finite field is introduced and some of its properties are presented.
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