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.
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.
Alireza F., Trong T.D., Chedjou J.C., and Kyamakya K. New Computational Modeling for Solving Higher Order ODE based on FPGA. Alpen-Adria University of Klagenfurt, Austria, 1-5, 2012.
ef{fig:sevoltage} show that circuits are more vulnerable to soft errors. As supply voltage decreases, the soft error rate increases.
[7] K. Anil Jain, Jianchang Mao and K.M. Mohiuddi, 1996. “Artificial Neural Networks: A Tutorial”, IEEE Computers, pp.31-44.
If a white pixel satisfies the conditions of the filtering algorithm, we then apply the Sobel edge
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).
...are. The inputs have to essentially come from the field, like from frequently performed the flight and ground scrutiny or unique mission calibrations. The obvious advantage from better measurement receivers against their defined presentation in self-motivated conditions is fully analogous measurement consequences This get better the security level of the deep-rooted ILS technology, in spite of today’s rising complexity in preserve reputable ILS service levels. We have analyzed and designed FIR filter’s with DC and other response to get in depth study of the problem. Our aim is to search for a cost and computationally effective technique for this task.
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...
An article written by MindShift titled “What’s the Impact of Overzealous Internet Filtering in Schools?” Quotes a statement from Kristen Batch saying “The over-filtering that occurs today affects not only what teachers can teach but also how they teach. It creates barriers to learning and acquiring digital literacy skills that are vital for college and career readiness, as well as for full participation in 21st-century society.” This supports the idea of over restrictive web filters, not only do they decrease ways of learning but they are seen as a “barrier”. Some may feel that these should not be referred to as restrictions, but something a bit more broad such as censorship. Reasons and point of views such as these explain why many may see restrictions as way too restrictive of what students and teachers can access to increase their learning
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Dadda proposed an algorithm with predetermined sequence of matrix (stage) heights for NxN multipliers to have reduced number of reduction stages. It is developed by working back from two row stage. The height of each intermediate stage is limited to floor value of 1.5 times the height of the successor stage [9].
Velocity of money is assumed to remain more or less stable in the long run.
Multiplier is key fundamental component for many high performance systems such as FIR-filters, microprocessors, digital processors, multimedia applications etc. Multiplier plays main role in system performance [3] [4] [5] because multiplier is generally the slowest element in the system. Furthermore, it occupied a large silicon area. Hence, optimizing speed and area are major design issues however area and speed both are conflicting performance constraints’.
But sometimes, such a linearization may lead to real errors not only of a quantitative but also of a qualitative nature. And when the linearization is not possible, the original nonlinear equation itself must be treated. With the discovery of numerous phenomena of self-excitation of circuits containing nonlinear capacitor of electricity, like electron tubes, gaseous discharge etc. and in many cases of nonlinear mechanical vibrations of special types, the method of small oscillations becomes inadequate for their analytical treatment[*]. To this end, a number of methods are developed, such as straight forward expansion method, Lindtsteadt-Poincare (LP) method, Modified LP method, Struble technique, Harmonic balance method, the Krylov-Bogoliubov-Mitropolskii (KBM) perturbation method
Ferguson et al. International financial stability. Geneva: International Center for Monetary and Banking Studies, 2007. Print.