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Math Help - Finding the transfer function (simultaneous equations)

  1. #1
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    Finding the transfer function (simultaneous equations)

    Hi, I have been staring at this all day and cannot solve it! It is a question for a DSP module. I have 5 equations and need to re-arrange them eliminating V1 - V4 so that I am left with Y(z)/X(z). I have attached an image with the equations. Could anybody help me out? It's driving me mad.

    Finding the transfer function (simultaneous equations)-la-foto-1.jpg
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  2. #2
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    Re: Finding the transfer function (simultaneous equations)

    Step 1. First substitute V_3 in equations (2) and (4) with the expression given in the equation (3).

    Step 2. Next, in the equation (5) express V_2. Use that expression as a substitution for V_2 in equation (4). Now equation (4) should represent V_4 in terms of z's, k's and Y(z).

    Step 3. Next use the expression for V_4 in equation (4) as a substitution for V_4 in equation (1). Now equation (1) should give you the expression for V_1 in terms of z's,k's and X(z) and Y(z).

    Now you have to deal with the equation (2). Substitute V_1 with the expression in the equation (1) from the step 3. On the left side of the equation term V_2(z) substitute with the expression obtained from the equation (5) (see step 2.)
    After that that equation should contain no V's and I presume thats the equation you've been chasing all along?
    Thanks from danlewy
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