How do you get a symbolic answer for this z transform in MATLAB

I can't figure out how to type this in with the unit step delay

This is my current code:

syms n z;

F=ztrans(2*(n-2)+3*(n-3)*(1/(1-z^-1)));

F2=collect(F);

[num, dem] = numden(F2)

pretty(F2)

Ts=0.1;

H=tf(sym2poly(num),sym2poly(dem),Ts);

pzmap(H)

Answer 1

[Star Strider]

If I remember correctly, the z-transform of theDirac delta funciton is 1, so:

syms x n x(n) z 
x(n) = 2*dirac(n-2) + 3*heaviside(n-3)
X = ztrans(x, n, z)
X = subs(X, {ztrans(dirac(n), n, z)}, {1})

producing:

X =
3/(z^3*(z - 1)) + 2/z^2

Continuing:

Xe = expand(X);
[num,den] = numden(Xe);
num = simplify(num, 'Steps',10)
den = simplify(den, 'Steps',10)
nd = sym2poly(num);
dd = sym2poly(den);

Ts = 0.1;
H = tf(nd, dd, Ts)

figure
bode(H)

figure
pzmap(H)

creates the Control System Toolbox ‘H’ system object, and the plots.

Answer 2

[Paul]

With the default symbolic preferences

sympref('default');

We have

heaviside(0),disp(char(ans))

ans = 0.5000

So the discrete-time unit step function is (we could also change the sympref so that heaviside(0) = 1)

syms x n x(n) u(n) z 
u(n) = heaviside(n) + kroneckerDelta(n)/2;

Define x[n] and take its z-transform

x(n) = 2*kroneckerDelta(n-2) + 3*u(n-3);
X = ztrans(x, n, z);
[num,den] = numden(X);X = num/den,pretty(X)

  2 z + 1
----------
 2
z  (z - 1)