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barcode generator for ssrs the closedloop system function is in Software
the closedloop system function is Code128 Recognizer In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. USS Code 128 Maker In None Using Barcode creator for Software Control to generate, create ANSI/AIM Code 128 image in Software applications. TRANSFORM ANALYSIS O F SYSTEMS
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H (z) = Placed in a feedback network with
I 1  1.22' G(z) = K the system function of the closedloop system is
which has a pole at z = 1.2/(1 + K). Therefore, this system will be stable for all K
s 0.2. Solved Problems
System Function
If the input to a linear shiftinvariant system is
the output is
~ ( n= 6 ( ; ) " u ( n )  6 ( : ) " u ( n ) ) Find the system function, H ( z ) , and determine whether or not the system is stable and/or causal.
CHAP. 51
TRANSFORM ANALYSIS OF SYSTEMS
In order to find the system function, recall that H ( z ) = Y ( z ) / X ( z ) . Because we are given both x ( n ) and y ( n ) , all that is necessary to find H ( z ) is to evaluate the ztransform of x ( n ) and y ( n ) and divide. With Then, For the region of convergence of H ( z ) , we have two possibilities. Either lzl z $ or Izl < Because the region of convergence of Y ( z ) is Izl > and includes the intersection of the regions of convergence of X ( z ) and H ( z ) , the region of convergence of H ( z ) must be lzl > Because the region of convergence of H ( z ) includes the unit circle, h ( n ) is stable, and because the region of convergence is the exterior of a circle and includes z = m, h ( n ) is causal. When the input to a linear shiftinvariant system is
the output is
A n ) = [4(;)" Find the unit sample response of the system.
 3(:)"]u(n) One approach that we may use to solve this problem is to evaluate H ( z ) = Y ( z ) / X ( z ) and then compute the inverse ztransform. Note, however, that we are given the response of the system to a step with an amplitude of 2, and we are asked to find the unit sample response. Because if we let s ( n ) be the step response, it follows from linearity that
h ( n ) = s ( n )  s(n  1) Therefore, from the response given above, we have
A causal linear shiftinvariant system is characterized by the difference equation
y(n) = by(n  1 ) + i y ( n  2) + x(n)  x(n  1 ) Find the system function, H ( z ) , and the unit sample response, h ( n ) . To find the system function, we take the ztransform of the difference equation, Y(z)= f z  ' ~ ( z ) $ Z  ~ Y ( Z ) X(z)  zIx(z) TRANSFORM ANALYSIS OF SYSTEMS
[CHAP. 5
Therefore, the system function is
Because the system is causal, the region of convergence is lzl z f . To find the unit sample response, we perform a partial fraction expansion of H ( z ) , where
Therefore. and the unit sample response is
A causal linear shiftinvariant system has a system function 1 z' I  izl
H (z) = Find the ztransform of the input, x(n), that will produce the output
I y(n) =  7 ( z )I " ~ ( n  +(2)"u(n ) To find the input to a linear shiftinvariant filter that will produce a given output y ( n ) , we use the relationship Y(z) = H(z)X(z) to solve for X(z): Computing the ztransform of y(n), we have Y (z) =  + A 1I 1  22' I 4  I (1 + fz'  izl)(l  2z1) Therefore, X(z) = (1 (1 + izI)(1  ;z1)  $z')(l  2z')(I + zI) 1 2 B C +  + I  2z1 I + z1 CHAP. 51
TRANSFORM ANALYSIS OF SYSTEMS
where
Because h ( n ) is causal, the region of convergence for H ( z ) is Izl > With the region of convergence of Y ( z ) the annulus < 15 1 i2, the region of convergence of X ( z ) is < IzJ i1. Therefore, Show that if h ( n ) is real, and H ( ) is rational, z
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