The convolution operation used in deterministic network calculus differs from its counterpart known from the classic systems theory. A reason for this lies in the fact that the former is defined in terms of the so-called min-plus algebra. Therefore, it is oft difficult to realize how it really works. In these cases, its graphical interpretation can be very helpful. This paper is devoted to a topic of construction of the min-plus convolution curve. This is done here in a systematic way to avoid arriving at non-transparent figures that are presented in publications. Contrary to this, our procedure is very transparent and removes shortcomings of constructions known in the literature. Some examples illustrate its usefulness.
This paper tries to get a response to the following question: When can a narrowband power amplifier (PA) be considered to be memoryless and when can it not be considered memoryless? To this end, a thorough and consistent analysis of the notions and definitions related with the above topic is carried out. In the considerations presented, two models of the narrowband PA are exploited interchangeably: the black box model widely used in the literature and a model developed here, which is based on the Volterra series. These two models complement each other. In this paper, the conditions for a linear or nonlinear narrowband PA to be memoryless or approximately memoryless or possessing memory are derived and illustrated. They are formulated in terms of the signal delay as well as in terms of the amplitude-to-phase (AM/PM) conversion of the amplifier. Furthermore, the two possible interpretations of the amplitude-to-amplitude (AM/AM) and AM/PM conversions are given a mathematical framework. That is these conversions are presented through some operations. One set of these operations allows to treat the AM/AM and AM/PM conversions as distortions of the modulating signals. Or equivalently as distortions of a given signal constellation when it passes through the PA. Finally, it is proved that the Saleh’s and Ghorbani’s models of the AM/AM and AM/PM conversions occurring in the PAs, which were published in the literature, are not memoryless ones.
This paper describes a “distributed method” of introducing the humanitarian engineering principles and concepts to the curriculum of telecommunications at a maritime university. That is by modifying appropriately the syllabi of the telecommunications subjects taught. The propositions made in this area are illustrated by the concrete examples taken from the current Polish Qualifications Framework for the higher education system in Poland. And, for clarity and consistency of presentation, fundamentals and principles as well as a basic terminology and features of this Framework are also highlighted here shortly. Moreover, it has been shown that the approach presented in this paper is more useful compared to a method based on organization of some special courses for students on the humanitarian engineering, in particular when this regards a maritime university.
In this paper, we present some useful results related with the sampling theorem and the reconstruction formula. The first of them regards a relation existing between bandwidths of interpolating functions different from a perfectreconstruction one and the bandwidth of the latter. Furthermore, we prove here that two non-identical interpolating functions can have the same bandwidths if and only if their (same) bandwidth is a multiple of the bandwidth of an original unsampled signal. The next result shows that sets of sampling points of two nonidentical (but not necessarily interpolating) functions possessing different bandwidths are unique for all sampling periods smaller or equal to a given period (calculated in a theorem provided). These results are completed by the following one: in case of two different signals possessing the same bandwidth but different spectra shapes, their sets of sampling points must differ from each other.
An available bandwidth at a link is an unused capacity. Its measuring and/or estimation is not simple in practice. On the other hand, we know that its continuous knowledge is crucial for the operation of almost all networks. Therefore, there is a continuous effort in improving the existing and developing new methods of available bandwidth measurement and/or estimation. This paper deals with these problems. Network calculus terminology allows to express an available bandwidth in terms of a service curve. The service curve is a function representing a service available for a traffic flow which can be measured/estimated in a node as well as at an endto- end connection of a network. An Internet traffic is highly unpredictable what hinders to a large extent an execution of the tasks mentioned above. This paper draws attention to pitfalls and difficulties with application of the existing network calculus methods of an available bandwidth estimation in a real Internet Service Provider (ISP) network. The results achieved in measurements have been also confirmed in simulations performed as well as by mathematical considerations presented here. They give a new perspective on the outcomes obtained by other authors and on their interpretations.