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barcode lib ssrs SIGNALS AND SYSTEMS in Software
SIGNALS AND SYSTEMS USS Code 128 Scanner In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. ANSI/AIM Code 128 Maker In None Using Barcode printer for Software Control to generate, create Code 128B image in Software applications. Because we are assuming zero initial conditions, y( 1) = 0, and because the input consists of a linear combination of a scaled unit sample and a scaled delayed step, the solution to the difference equation is simply Decoding ANSI/AIM Code 128 In None Using Barcode decoder for Software Control to read, scan read, scan image in Software applications. Make USS Code 128 In C#.NET Using Barcode drawer for VS .NET Control to generate, create Code 128A image in .NET framework applications. where h(n) and s(n) are the unit sample and unit step response, respectively. To find the unit sample response, we write the difference equation in the form Create ANSI/AIM Code 128 In VS .NET Using Barcode generator for ASP.NET Control to generate, create Code 128C image in ASP.NET applications. USS Code 128 Drawer In Visual Studio .NET Using Barcode encoder for VS .NET Control to generate, create Code 128A image in .NET framework applications. The characteristic equation for this difference equation is
Draw Code 128 Code Set B In Visual Basic .NET Using Barcode drawer for Visual Studio .NET Control to generate, create Code 128 Code Set A image in .NET framework applications. Make GTIN  128 In None Using Barcode creator for Software Control to generate, create UCC.EAN  128 image in Software applications. and the homogeneous solution is y(n)=Avn n>O Because the input x(n) = S(n) is equal to zero for n > 0, the particular solution is zero (all that the unit sample does is set the initial condition at n = 0). Evaluating the difference equation at n = 0, we have Code 39 Extended Encoder In None Using Barcode creator for Software Control to generate, create Code 3/9 image in Software applications. Bar Code Drawer In None Using Barcode encoder for Software Control to generate, create bar code image in Software applications. Therefore, it follows that A = 1 in the homogeneous solution, and that the unit sample response is
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Draw Code 39 Full ASCII In None Using Barcode creation for Font Control to generate, create Code 39 Full ASCII image in Font applications. Code 3/9 Generator In None Using Barcode drawer for Word Control to generate, create Code 39 Full ASCII image in Microsoft Word applications. With v = % and p = 100,000, we have d = 877.57 The total payment to the bank after 30 years is C = (877.57)(360) = 315,925.20 Every second, each a particle within a reactor splits into eight P particles and each , 3 particle splits into L Y an L particle and two P particles. Schematically, a+8P Pa+2/3 SIGNALS AND SYSTEMS
[CHAP. 1
Given that there is a single a particle in the reactor at time n = 0, find an expression for the total number of particles within the reactor at time n. Let a ( n ) and B ( n ) be the number of a particles and B particles within the reactor at time n. The behavior within the reactor may be described by the following pair of coupled difference equations: Before we can solve these difference equations, we must uncouple them. Therefore, let us derive a single difference equation for B(n). From the first equation we see that a ( n ) = # (n  I). Substituting this relation into the second difference equation, we have B(n+ 1)=8B(n1)+2B(n) or, equivalently, B ( n ) = 2B(n  0 The characteristic equation for this difference equation is
+ 8B(n
 2) which gives the following homogeneous solulion
Similarly, because a ( n ) = B(n  I), the solution for a ( n ) is
With the initial conditions a ( 0 ) = I and B(0) = 0, we may solve for A1 and A2 as follows: and the solutions for a ( n ) and B ( n ) are
a ( n ) = i(4)" B ( n ) = :(4)" + !(2)"  (2)" 3 n 20 n 20
Because we are interested in the total number of particles within the reactor at time n , with
Supplementary Problems
DiscreteTime Signals 1.41
Find the period N of the sequence
CHAP. 11
SIGNALS AND SYSTEMS
The input to a linear shiftinvariant system is periodic with period N . (a) Show that the output of the system is also periodic with period N. (b) If the system is linear but shiftvarying, is the output guaranteed to be periodic (c) If the system is nonlinear but shiftinvariant, is the output guaranteed to be periodic 1.43 1.44 If x(n) = 0 for n < 0, and the odd part is x,,(n) = n(0.5)1n1, x(n) given that x(0) = 1. find Find the conjugate symmetric part of the sequence 1.45 1.46 If x(n) is odd, what is y(n) = x2(n) If x(n) = 0 for n < 0, Pe is the power in the even part of x(n), and Po is the power in the odd part, which of the following statements are true (a) Pc Po (b) Po 2 Pe (c) Pe = Po (d) None of the above are true.
Express the sequence x(n) = as a sum of scaled and shifted unit steps. (1 (0 2 5 11 5 2 else
Synthesize the triangular pulse
as a sum of scaled and shifted pulses, DiscreteTime Systems
Listed below are several systems that relate the input x(n) to the output y(n). For each, determine whether the system is linear or nonlinear, shiftinvariant or shiftvarying, stable or unstable, causal or noncausal, and invertible or noninvertihle. (e) y(n) = median(x(n  l), x(n), x(n
+ I)) SIGNALS AND SYSTEMS
[CHAP. 1
Given below are the unit sample responses of several linear shiftinvariant systems. For each system, determine the conditions on the parameter a in order for the system to be stable. (a) h ( n ) = a n u (  n ) (h) h ( n ) = a " [ u ( n ) u(n  100))

