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## Solution manual for linear system and signal

(2.41) and (2.43) associated with.

This is a consequence of assuming that the input is zero prior to July 31, 1998.

We thus write d q1t2 Aq1t2 bx1t2 dt (2.64) y1t2 cq1t2 Dx1t2.

(b) Find a transformation of the state that will diagonalize.That is, we construct System Output 12 10 8 Amplitude HAY-02A-097-194.I Time figure.46 Solution to Problem.29.Solution: First, we graph x3k4 and h3n - k4, treating n as a constant and k as the independent variable, as depicted in Fig.This procedure is summarized as follows: Procedure.3: Solving cronulla riots the day that.rar a Differential or Difference Equation.Accordingly, let us interchange their order and denote the output of the new first system as f 3n4.The third system representation we discuss is the block diagram, which represents the system as an interconnection of three elementary operations: scalar multiplication, addition, and either a time shift for discrete-time systems or integration for continuous-time systems.HAY-02A-097-194.I 154 8/20/02 10:21 AM chapter 2 Page 154 time-domain representations OF linear time-invariant systems The input does not introduce impulses into the right-hand side of the differential equation, so the coefficient c is determined from the initial condition y10-2 y102.For n Ú 0, we may write the mathematical representation of wn3k4 as wn3k4 b 100011.082n - k, 0.Dt Find the forced response of this system, assuming that x1t2 cos1t2u1t2 V, R 1 Æ, and C.(b) The product signal w-53k4 used to evaluate y3-54.Now we use y304 1 to solve for c1 from the equation a b c1 a b, 2 4 HAY-02A-097-194.I 8/20/02 10:21.11 Page 159 Characteristics of Systems Described by Differential and Difference Equations 159 which implies that c1 -1.

Combining the solutions for the three intervals of time shifts gives the output y1t2 c 0, t 6 0 1 - e -t, 0 t 6 2, 2 -t 1e - 12e, t Ú 2 as depicted in Fig.

2.35 is termed a direct form II implementation.

Skip to main content, academia.In general, the mathematical representation of wt1t2 depends on the value.(2.33) Since hinv304 1,.R 1 100 Thus, we find that interest calculations involve an unstable system.Differential equations are used to represent continuous-time systems, while difference equations represent discrete-time systems.2.13(a) that x1t2 b 1, 0 6 t 6 2 0, otherwise and h1t - t2 e -1t - t2u1t - t2 b e -1t - t2, t.Solution: We write the new state vector as q œ Tq, where T 1 -1 1.Each block diagram representation describes a different set of internal computations used to determine the system output.

HAY-02A-097-194.I 8/20/02 10:20.10 Page 149 149 Solving Differential and Difference Equations The parameter r1 is obtained from the root of the characteristic equation given.

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2.44 Show that if y1t2 x1t2 * h1t2 is the output of an LTI system with input x1t2 and impulse response h1t2, then (ii) RC 5 gt;T d d y1t2 x1t2 * a h1t2 b dt dt (iii) RC 1 gt;15T2 R p(t) x(t) y(t).

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