This paper proposes a new criterion for the input/output-to-state stability (IOSS) of interfered direct-form digital filters with finite wordlength nonlinearity based on an augmented Lyapunov function. Without external interference, the output-to-state stability (OSS) and asymptotic stability of direct-form digital filters with finite wordlength nonlinearity are also guaranteed under the proposed criterion. This criterion is expressed by linear matrix inequalities (LMIs). A numerical example demonstrates the effectiveness of the proposed criterion.
Key Words: input/output-to-state stability (IOSS); output-to-state stability (OSS); asymptotic stability; digital filter; finite wordlength effect
1 Introduction
When we design and implement digital filters, we use fixed-point arithmetic, which generates overflow and quantization nonlinearities. These nonlinearities can cause the digital filters potentially to produce zero-input limit cycles if the coefficients of the digital filters are not selected appropriately [?]. Zero-input limit cycles are an unstable behavior and should be avoided in digital filter design [?]. Thus, the range determination of the coefficients of digital filters, where these limit cycles should be avoided, is very important. Much attention has been focused on the criteria for the removal of limit cycles in digital filters, including overflow nonlinearity [?, ?, ?, ?, ?, ?, ?, ?, ?, ?]. When we implement a high-order large scaled digital filter using hardware and digital computers, we usually break it down into several low-order digital filters before implementation. In this case, mutual interferences inevitably occur between these low-order filters, and this leads to malfunction as well as poor perfo...
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...hich guarantee the IOSS when and the OSS and asymptotic stability when in this example. Let . Figure 1 shows that the state variables are bounded around the origin by the IOSS property when , where is a white Gaussian random sequence with mean and variance . Figure 2 shows that the state variables converge to the origin when .
Figure 1: Phase plot when
Figure 2: Phase plot when
5 Conclusion
In this paper, we have proposed a new LMI based criterion for the IOSS of interfered direct-form digital filters with saturation overflow nonlinearity. Based on the augmented Lyapunov function, the criterion also guarantees the OSS and asymptotic stability of direct-form digital filters without external interference under the additional LMI condition. The criterion is expressed by LMIs. An example was provided to demonstrate the proposed criterion.
Fuzzy Trace theory functions and serves as a better model for explicating reasoning and decision making. There are five parts of “processing in reasoning and decision making: (a) stored knowledge and values; (b) mental representations of problems or situations; (c) retrieval of knowledge and values; (d) implementation of knowledge and values; and (e) developmental and individual differences in monitoring and inhibiting interference” (Reyna & Brainerd, Dual Processes in Decision Making and Developmental Neuroscience: A Fuzzy-Trace Model, 2011). Stored knowledge implies what has been stored in long-term memory through education and experience. Mental representations incorporate the ways in which people perceive problems to be faced, and these representations consist of verbatim- and gist-based representations.
Class I CAs evolve4 to a uniform configuration of cell states, from nearly any initial configuration. This state can be thought of in dynamical systems terms as a ‘point attractor’, or ‘limit point’. As one would suspect, the rules for class I CAs map from most or all possible neighbour configurations to the same new state. Initial lattice configurations do exist for some class I CAs that lead to non-trivial cycles, but these are very rare.
...cal techniques which are numerically stable and can be used to both linear and nonlinear fractional differential equation [28]have been developed in the literature. For finding the numerical approximation more accurate and for reducing the computational cost here we choose the Caputo version and predictor-corrector algorithm for fractional differential equation [29],.According to the fractional predictor-corrector algorithm, we find that hyper chaos exist in new four-dimensional fractional order system. In the numerical results the system parameters are chosen as a = 10, b = 28, c = 8/3 and d = 1. Numeric results shows that when 0.9 1, the fractional- order system (2) always exhibits hyper chaotic behaviors. The two Lyapunov exponents τ_1=0.9,τ_2=0.08 are obtained when = 0.9 is chosen. If < 0.9 then in system (2) there is no hyper chaos exist. As shown
...ics, a manual computation of successive RR intervals is resorted to. This series of RR intervals is subjected to both time domain and frequency domain analyses.
In control and communication engineering fields, filtering problems appears when the measurement of the system is not adequate due to the noise appearance or other disturbance. A filtration technique is used to obtain a more valuable information from a non ideal measurement. It can be formulated in sense of Bayesian projection of given set of measurement history, so called filtration, or any other sense of the optimality, like H-infinity norm.
I don't think that web filters are too restrictive, but they don't block the right things. One example is my school's web filters blockage of coolmath.com, a math learning website because one part the site includes an active chatroom. The web filter doesn't block a gaming website known as Friv. I believe that a teacher should have access to the web filter so a student can go to them and ask for permission to go to a site that's relevant to what they are studying in class but would be blocked universally on the school network. This should also work so if a student is on a gaming site the teacher can block it right away and bring the student back on topic. The teacher should then be able to let the school know about it so they can universally
...easures pertaining to the micro stability of the intermediaries can be subdivided into two categories; general rules on the stability of all business enterprises and entrepreneurial activities, such as the legally required amount of capital, borrowing limits and integrity requirements; and more specific rules due to the special nature of financial intermediation, such as risk based capital ratios, limits to portfolio investments and the regulation of off-balance activities. [White 1996] References Z Bodie, A Kane and A J Marcus. "Investments". 5th Ed. Irwin 2000. E J Elton and M J Gruber. "Modern Portfolio Theory and Investment Analysis". John Wiley 5th Edition 1995. White L., 1996, "International Regulation of Securities Markets: Competition or Harmonization?” in Lo A. (ed), The Industrial organization and Regulation of the Securities Industry, NBER, Cambridge
If a white pixel satisfies the conditions of the filtering algorithm, we then apply the Sobel edge
As capitalism runs its course and develops new technologies, society is left to pick up the pieces and figure out where these new technologies will lead them. Ever since I learned to use the Internet as a child, I have become accustomed to seeing more and more fascinating technology developments that have changed the way I communicated as the years went by. Now that the Internet has infiltrated more aspects of human life, it has become necessary to reflect on how this critical juncture will continue to affect our society. In Digital Disconnect, Robert McChesney provides an analysis of the arguments that the celebrants and skeptics used to express their views of the Internet. McChesney then moves past these arguments to explain how the PEC plays a key role in determining the direction that the Internet is heading towards. By assessing McChesney’s views, I hope to develop my own interpretation of the Internet’s impact on society.
Firewalls check incoming traffic against their own filters, which are set by the firewall's software company. It works similarly with outgoing traffic; if your computer is infected with a virus and tries to send instructions to other computers via your network, the software firewall will keep it contained (Wright, n.d., para 3).
Ayre (2004) in her overview of the history of filtering she mentions that filters were designed for parents, schools and business and have been influenced largely by religious groups and employers whose filter requirements
The uses of Digital Signal Processing in communications has become so large scale that nearly any form of analog communication is considered obsolete. Today, nearly any form of communication used, aside from verbal communication, relates to Digital Signal Processing. Some of the more prominent uses for DSP in communications are; local area networks, cell pho...
Nonlinear relationship is also a key principle of chaos theory (Hudson, 2000). According to Hudson (2000), nonlinearity is necessary for chaos. It shows the disproportion of cause and eff...
Ferguson et al. International financial stability. Geneva: International Center for Monetary and Banking Studies, 2007. Print.