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Convolution - Rutgers University

Systematrest(zero initialconditions)duetoanyinputistheconv olutionofthatinputandthesystemimpulseres ponse. Wehavealreadyseenandderivedthisresultint hefrequencydomaininChapters3,4,and5,henc e,themainconvolutiontheoremis applicableto, anddomains,thatis,it , , PrenticeHall, and isdefinedby Inthisintegralisa dummyvariableofintegration,andisa ,wefirstintroducethenotionofthesignaldur ation. Thedurationofa signal isdefinedbythetimeinstants and forwhichforeveryoutsidetheinterval thesignalis equaltozero,thatis, , . Signalsthathavefinitedurationareoftencal ledtime-limitedsignals. Forexample,rectangularandtriangularpulse saretime-limitedsignals, :Theslidescontainthecopyrightedmaterialf romLinearDynamicSystemsandSignals, PrenticeHall, 21)Commutativity 2)Distributivity 3)Associativity 4)DurationLetthesignals and havethedurations,respectively,definedbyt hetimeintervals and then Theslidescontainthecopyrightedmaterialfr omLinearDynamicSystemsandSignals, PrenticeHall, 35)TimeShiftingLet

that is, it is applicable to both continuous-and discrete-timelinear systems. In this chapter, we study the convolution concept in the time domain. The slides contain the copyrighted material from Linear Dynamic Systems and Signals, Prentice Hall, …

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9.6 Correlation of Discrete-Time Signals - Rutgers University

eceweb1.rutgers.edu

9.6 Correlation of Discrete-Time Signals A signal operation similar to signal convolution, but with completely different physical meaning, is signal correlation. The signal correlation operation can be performed either with one signal (autocorrelation) or between two different signals (crosscorrelation).

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bk1 - Rutgers University

eceweb1.rutgers.edu

14 S-Parameters 14.1 Scattering Parameters Linear two-port (and multi-port) networks are characterized by a number of equivalent circuit parameters, such as their transfer matrix, impedance matrix, admittance matrix,

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signs. In fact, historically, these methods were first developed in antenna theory and only later were adopted and further developed in DSP. 22.2 Translational Phase Shift The most basic property of an array is that the relative displacements of the antenna ele-ments with respect to each other introduce relative phase shifts in the radiation ...

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9.6 Correlation of Discrete-Time Signals A signal operation similar to signal convolution, but with completely different physical meaning, is signal correlation. The signal correlation operation can be performed either with one signal (autocorrelation) or between two different signals (crosscorrelation).

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