Z Trandform matlab input

I have the following equation:

x(n)= 3(0.25^n)u(n)-(0.75^(n-1))u(n-1)

hot would I input this to solve using matlab?

[Christopher Guerrero]

More specifically sorry for not putting this I am looking for how to put this in and get the ztransform answer out.

Answer 1

[Star Strider]

If you have the Symbolic Math Toolbox:

syms n t z 
u(n) = heaviside(n);
x(n)= 3*(0.25^n)*u(n)-(0.75^(n-1))*u(n-1);
X = ztrans(x, n, z);                                        % Z-Transform
[Xn,Xd] = numden(X);
Xd = expand(Xd);
H(z) = Xn / Xd;                                             % Transfer Function

H(z) =
-(- 48*z^3 + 40*z^2 + 17*z - 3)/(32*z^3 - 32*z^2 + 6*z)

[Christopher Guerrero]

How can i get the z transform answer

[Christopher Guerrero]

>> syms n t z >> u(n) = heaviside(n)

u(n) =

heaviside(n)

>> x(n)= 3*(0.26^n)*u(n)-(-0.75^(n-1))*u(n-1)

x(n) =

3*(13/50)^n*heaviside(n) + (3/4)^(n - 1)*heaviside(n - 1)

>> x = ztrans(x, n, z)

x(z) =

(1/((4*z)/3 - 1) + 1/2)/z + 3/((50*z)/13 - 1) + 3/2

>> pretty(x)

     1 
  ------- + 1/2 
  4 z 
  --- - 1 
   3                 3 
  ------------- + -------- + 3/2 
        z         50 z 
                  ---- - 1 
                   13

I used this for just the z transform does this look correct?

[Star Strider]

That looks like a continued fraction expansion of some sort. The approach I took created what appears to be a transfer function with distinct numerator and denominator polynomials.

I’ve not done a hand version of the conversion of a difference equation to a z-transform in decades. I’m comfortable with whatever the Symbolic Math Toolbox calculates!