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

    Distinguished Member

    Jun 17, 2014
    2,573
    522
    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

    Distinguished Member

    Jun 17, 2014
    2,573
    522
    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

    Distinguished Member

    Jun 17, 2014
    2,573
    522
    Hi again,

    That looks reasonable :)
     
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