formula mathematical

[saifizi]

Dear All,

I want to know how to solve the polynomial equation and define the parameter of the equation. Above is my equation that have to solve;

(1+f1*z^-1+f2*z^-2)(a0+a1*z^-1+a2*z^-2)+(z^-1)(b0+b1*z^-1+b2*z^-2)(g0+g1*z^-1+g2*z^-2)=1+t1*z^-1+t2*z^-2

From that equation, I have/know the parameter of a0, a1, b1, b2, t1 and t2. I have to solve the equation to get the parameter  f1, f2, g0, g1 and g2. I don't know the suitable mathematical labview programming can easily help me solve that equation. Thank you for all give time for my problem.

[saifizi]

Dear All, I hope some can help me or give some advise or some example that I can go through to apply for the equation. Thank you very much.

[Dennis_Knutson]

First of all, you need to show a little patience. Expecting an instant response is not reasonable. Second, you posted to the Instrument Control board. You should have posted to the LabVIEW board.

[crossrulz]

I advice trying to work this out by hand first.

1.  Expand the polynomials.  You will get something really long.  Now for the cool trick

2.  Take all of the z^0 from one side and set it equal to all of the z^0 on the other side of the equation.  You should get a0 = 1.  Do the same for the z^-1 and so on.  Here are the equations I ended up with.  You really should double-check my math.  I kind of did it in a hurry and I might have made some typos.

z^0: a0 = 1

z^-1: a2 + a0*f1 + b0*g0 = t1

z^-2: a2 + a1*f1 + a0*f2 + b0*g1 + b1*g0 = t2

z^-3: a2*f1 + a1*f2 + b0*g2 + b1*g1 + b2*g0 = 0

z^-4: a2*f2 + b1*g2 + b2*g1 = 0

z^-5: b2*g2 = 0

So what does this tell us?  Well, first of all, if b2 is not 0, then g2 must be 0.  a0 must be 1.  Reduce the equations as values are figured out.  I have a feeling you will still have to choose some value for a g or f.

[Bob_Schor]

I really don't think that LabVIEW is the appropriate software for solving this problem.  I'm not certain quite what you need, but something that does symbolic math (so you can write your equation down and ask it to simplify it for you, to expand it, to "solve for Z in terms of ...", would seem more appropriate than a Laboratory Virtual Instrument Engineering Workbench.  I'd recommend one of the "M" packages (Mathematica, Maple, MapLab, MathCad).

[crossrulz]

I have to agree with Bob here.  Matlab with the symbolic toolbox or Mathematica (those are the two I'm worked a little bit with) would help you a lot.  But looking at my equations again, assuming b2 is not 0, then there are 4 equations and 4 unknowns (f1, f2, g0, g1).  You should be able to solve them with some fun algebra.

[saifizi]

Thank you for your advise. I will try to solve it using matrix sylvester.

[Alexander_Sobolev]

Linear equations. Do you need a symbolic form of the inverse 4x4 matrix? I suppose it is easier (in most cases) to solve it when you know values of a-s and b-s. Any mathematical package can do it, including base LabVIEW.

[WG-]

Or use Wolfram|Alpha

http://www.wolframalpha.com/input/?i=%281%2Bf1*z%5E-1%2Bf2*z%5E-2%29%28a0%2Ba1*z%5E-1%2Ba2*z%5E-2%29...

[paul_a_cardinale]

You have one equation and five unknowns.  There is no single solution.  There is an infinte set of values for f1, f2, g0, g1 and g2 that will satisfy the equation.