The mean power spectral density of Markov chain driven signals
TL;DR: In this paper, the mean power spectral density function of a signal driven by a stationary discrete-parameter finite-state Markov chain is derived and discussed, both for irreducible and reducible chains.
Abstract: Many signals ocurring in data communications can be described by Markovian models. Expressions for the mean power spectral density function of a signal driven by a stationary discrete-parameter finite-state Markov chain are derived and discussed, both for irreducible and reducible chains. Two examples are presented to illustrate the application of the results.
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01 Jan 1999
372 citations
Cites methods from "The mean power spectral density of ..."
...Invoking the definitions given in Chapter 2, and by virtue of the assumed ergodicity of the Markov chain described therein, we can write down the auto-correlation (see Bilardi, Padovani & Pierobon [31] and Galko & Pasupathy [107])...
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20 Jun 1993
TL;DR: In this article, the power spectra of signals are used to classify randomized modulation schemes for DC/DC converters, and a general spectral formula for stationary randomized modulation is presented.
Abstract: After establishing that the proper objects of study for randomized modulation of converters are the power spectra of signals, we classify such modulation schemes and present associated spectral formulas, several of which are new. We also discuss numerical (Monte Carlo) verification issues for power spectral formulas. A general spectral formula for stationary randomized modulation schemes is presented, and specialized to several modulation schemes of practical interest for DC/DC converters. Analytical results are then given for block-stationary randomized modulation schemes that are suitable for inverter operation. In the process, we present results for several modulation schemes that have been reported in the literature without analytical explanations. Experimental verifications of some of our analytical results are presented. We formulate narrow-band and wide-band synthesis problems in randomized modulation, and solve them numerically. Our results suggest that randomized modulation is very effective in satisfying narrow-band power constraints, but has limited effectiveness in meeting wide-band constraints. >
207 citations
TL;DR: A pseudo-chaotic modulation suitable for ultrawide-bandwidth impulse-radio communication systems, based upon controlling the symbolic dynamics of a chaotic map for encoding the digital information to be transmitted.
Abstract: In this paper, we propose a pseudo-chaotic modulation suitable for ultrawide-bandwidth impulse-radio communication systems. The coding scheme is based upon controlling the symbolic dynamics of a chaotic map for encoding the digital information to be transmitted. The pseudo-chaotic time hopping enhances the spread-spectrum characteristics of the system, by removing most periodic components from the transmitted signal. A maximum-likelihood detector for the proposed scheme is presented and its scalability features are illustrated. Finally, theoretical performance bounds for both soft and hard Viterbi decoding are derived and compared with the simulation results.
142 citations
TL;DR: It is shown that the finite running digital sum condition is a necessary and sufficient condition for alphabetic codes to occur, which are the most widely used line codes in pulse-amplitude modulation systems.
Abstract: In pulse-amplitude modulation (PAM) digital transmission systems line encoding is used for shaping the spectrum of the encoded symbol sequence to suit the frequency characteristics of the transmission channel. In particular, it is often required that the encoded symbol sequence have a zero mean and spectral density vanishing at zero frequency. We show that the finite running digital sum condition is a necessary and sufficient condition for this to occur. The result holds in particular for alphabetic codes, which are the most widely used line codes.
132 citations
07 Aug 2002
TL;DR: The authors present results important for practice and to establish connections with several areas of applied probability, and consider the synthesis task for the two cases of randomized modulation.
Abstract: This article reviews analytical results and practical experience with randomized modulation in power electronic converters. After providing a brief overview of power electronics and of relevant switching patterns, the authors present performance specifications for converters (in terms of electromagnetic interference, vibrations and acoustic noise), and classify various randomized switching schemes. They review the most directly related references next, and introduce the mathematical objects of primary interest-averaged autocorrelation and power spectrum. They then list some results for the (simpler) case of stationary modulation and consider in detail the more general case of randomized switching based on Markov chains. Their aim is twofold-to present results important for practice and to establish connections with several areas of applied probability. Finally, they consider the synthesis task for the two cases of randomized modulation, followed by brief conclusions.
90 citations
Cites background from "The mean power spectral density of ..."
...Some analysis results for waveforms generated in the fashion described here have been provided by communication theorists [5], [74], but applications in power electronics have not been suggested before [16], [18]....
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References
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16,450 citations
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01 Jan 1917
TL;DR: Basic Forms x n dx = 1 n + 1 x n+1 (1) 1 x dx = ln |x| (2) udv = uv − vdu (3) 1 ax + bdx = 1 a ln|ax + b| (4) Integrals of Rational Functions
Abstract: Basic Forms x n dx = 1 n + 1 x n+1 (1) 1 x dx = ln |x| (2) udv = uv − vdu (3) 1 ax + b dx = 1 a ln |ax + b| (4) Integrals of Rational Functions 1 (x + a) 2 dx = −
11,190 citations
TL;DR: A PRS system model is introduced which enables the investigation of PRS schemes from the viewpoint of spectral properties such as bandwidth, nulls, and continuity of derivatives and it is shown that eye width, a performance measure that has not been used previously in comparing PRS systems, can be calculated analytically in many cases.
Abstract: This paper presents a unified study of partial-response signaling (PRS) systems and extends previous work on the comparison of PRS schemes. A PRS system model is introduced which enables the investigation of PRS schemes from the viewpoint of spectral properties such as bandwidth, nulls, and continuity of derivatives. Several desirable properties of PRS systems and their relation to system functions are indicated and a number of useful schemes, some of them not previously analyzed, are presented. These systems are then compared using as figures of merit speed tolerance, minimum eye width, and signal-to-noise ratio (SNR) degradation over ideal binary transmission. A new definition of speed tolerance, which takes into account multilevel outputs and the effect of sampling time, is introduced and used in the calculation of speedtolerance figures. It is shown that eye width, a performance measure that has not been used previously in comparing PRS systems, can be calculated analytically in many cases. Exact values as well as bounds on the SNR degradation for the systems under consideration are presented. The effect of precoding on system performance is also analyzed.
507 citations