In the diagram above, R(z) is the z-transform of the system’s input r[n], C(z) is the z-transform of...

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In the diagram above, R(z) is the z-transform of the system’s input r[n], C(z) is the z-transform of thesystem’s output c[n], and G(z) and H(z) are the transfer functions of the subsystems given by:G(z) = z / (z+1)H(z) = 9 / (z-8)(a) Determine the unit-pulse response of the overall system. [3 marks](b) Compute the step response of the overall system. [3 marks](c) Compute c[n] when r[n]=(0.5)nu[n] with c[-1]=-3, c[-2]=4; Hint: In order to incorporate the initialconditions into your solution, you need to revert to the difference equation (hint: cross multiply the transferfunction). Once the difference equation is obtained, the z-transform can be taken to obtain the initialcondition terms. [8 marks](d) Compute c[n] when r[n]=(0.5)nu[n] with c[-2]=1, b[-1]=2, where b[n] is the output of block H(z); Hint:Determine c[-1] by obtaining a difference equation with c[n] and b[n] terms (you need an equation with C(z)and B(z)). Then substitute c[-1] into the result you obtained for C(z) in part (c). [6 marks]
	
Document Preview: Signal Theory XXXXXXXXXXAdvanced Assignment
Note: Please refer to the subject outline for details regarding the assessment of the advanced assignment.
Using the standard form of a feedback control system shown below, assume that the system to be studied is a
linear time-invariant discrete-time system.
In the diagram above, R(z) is the z-transform of the system’s input r[n], C(z) is the z-transform of the 
system’s output c[n], and G(z) and H(z) are the transfer functions of the subsystems given by:
G(z) = z / (z+1)
H(z) = 9 / (z-8)
(a) Determine the unit-pulse response of the overall system.   [3 marks]
(b) Compute the step response of the overall system.   [3 marks]
n
(c) Compute c[n] when r[n]=(0.5) u[n] with c[-1]=-3, c[-2]=4;  Hint: In order to incorporate the initial
conditions into your solution, you need to revert to the difference equation (hint: cross multiply the transfer
function). Once the difference equation is obtained, the z-transform can be taken to obtain the initial
condition terms.   [8 marks]
n
(d) Compute c[n] when r[n]=(0.5) u[n] with c[-2]=1, b[-1]=2, where b[n] is the output of block H(z);  Hint:
Determine c[-1] by obtaining a difference equation with c[n] and b[n] terms (you need an equation with C(z) 
and B(z)). Then substitute c[-1] into the result you obtained for C(z) in part (c).   [6 marks]
Warning
This assignment must be completed on an individual basis - that is, you cannot obtain help from other
students or from staff. (Your tutor is able, however, to help you in your understanding of the question.) 
Anyone found using someone else’s work will be subject to the disciplinary processes of the University. 
Please do not risk it.
1 of 2Please note also you must be able to explain your work (in detail) if asked to do so.  If you are unable to
do so, it will be assumed you have used someone else’s work and you will face the same disciplinary 
processes as above.  Again, it’s not worth the risk of receiving 0Z for the subject, or 0Z for...

Robert · Accepted Answer

Solution: 
A)  ( )  
 
   
 
 ( )  
 
   
 
Unit pulse response is: 
 ( )
 ( )
 
 ( )
   ( ) ( )
 
// Transfer function of a system is given by above formula 
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 ( )

  
 
   

 ( )
 ( )
 
 (   )
(   )(   )    
 
// Simplified transfer function is: 
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R(z)=1 
// Pulse response means that input R(z)=1 (similar to impulse response in laplace) 
Pulse response is: 
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 ( )
 

       
 
 ( )
 

          
 
 ( )
 

(   )(   )
 
// Partial fraction is: 
 ( )
 

   

   
 
 ( )  
  
   

   
 
 [ ]   (  )
B) Step response of system is 
// For step response the input r[n]=1 or R(z)=(z/(z-1)) 
 ( )  
 
     
 
//When we find step response of the system then the input is taken to be unit step.

In the diagram above, R(z) is the z-transform of the system’s input r[n], C(z) is the z-transform of thesystem’s output c[n], and G(z) and H(z) are the transfer functions of the subsystems given...

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