Simulation diagram from a Transfer function/difference equation

Discussion in 'Homework Help' started by josh007, Sep 3, 2016.

  1. josh007

    Thread Starter Member

    Sep 20, 2015
    40
    1
    Greetings,

    I require assistance.

    Calculate the difference equation and then Draw the simulation diagram of the below transfer function.

    H(z) = Y(z)/X(z) = (0,4142 + 0.4142(z^-1)) /(1,4142 - 05858(z^-1))


    I performed the normal procedure to find the difference equation, by cross multiplying and using the delay property of the z-transforms, I finally ended up with:

    y(n) = 0,2929x(n) + 0.2929x(n-1) + 0.4137y(n-1)

    How do I Draw the simulation diagram?

    I don't require the answer but guidance on how to derive the diagram and final answer.

    Thanks.

    Regards
    Joshy
     
  2. MrAl

    Well-Known Member

    Jun 17, 2014
    2,418
    488
    Hi,

    You can start by making n=0 and then increment it, 1,2,3, etc., up to the required last number where you see at least one cycle or whatever it shows.

    You might set y(0)=0 unless you have initial conditions and x(-n) equal to zero in most cases unless you have values for x(-n) and then you would have to run n lower than zero also. You also probably set y(-1)=0 too and all other y with n negative unless those have initial conditions also.

    The simulation could be a plot of all y(n) and x(n) just as you would with y=2*t where you plot y vs t, or you could plot y(n) vs n and perhaps y(n) and x(n) vs n (two plots with n running horizontal).
     
  3. josh007

    Thread Starter Member

    Sep 20, 2015
    40
    1
    Hi MrAI,

    I also wanted to know if my difference equation is correct?

    I will show u my working now.

    upload_2016-9-4_11-57-38.png
     
  4. MrAl

    Well-Known Member

    Jun 17, 2014
    2,418
    488
    Hi,

    That's not bad, but how are you getting 0.4137 when you divide 0.5858 by 1.4142 ?
    That comes out just a little different than what you show there right?
     
  5. josh007

    Thread Starter Member

    Sep 20, 2015
    40
    1
    Hi MrAI,

    you right sir thats wrong it should be y(n) = 0.2929x(n) + 0.2929x(n-1) + 0.4142y(n-1),

    I am going to take a pic of my block diagram now.

    Gracias.
    Joshy
     
  6. josh007

    Thread Starter Member

    Sep 20, 2015
    40
    1
    Hello,

    I have done this,

    upload_2016-9-4_15-15-14.png
     
  7. MrAl

    Well-Known Member

    Jun 17, 2014
    2,418
    488
    Hi again,

    That looks reasonable :)
     
Loading...