How to get the Z-transform and tf of this function y[n] = 0,5y[n − 1] + x[n] ?

I don't know ho to write on matlab this EDD function, after that i can use ztrans() and tf(), but i need to know how to write it on matlab first.

Answer 1

[Star Strider]

Perhaps something like this —

syms n x(n) y(n) z t X(z) Y(z) 
assume(n>=0 & in(n,"integer"))
Eqn = y(n) == 0.5*y(n - 1) + x(n)

Eqn = 

Eqn = ztrans(Eqn, n, z)

Eqn = 

Eqn = subs(Eqn, {ztrans(y(n),n,z), ztrans(x(n),n,z)},  {Y(z), X(z)})

Eqn = 

Eqn = isolate(Eqn, Y)

Eqn = 

[N,D] = numden(rhs(Eqn))

N = 

D = 

Nc = sym2cell(N)

Nc = 1x1 cell array
    {[z*y(-1) + 2*z*X(z)]}

Dc = sym2cell(D)

Dc = 1x1 cell array
    {[2*z - 1]}

I leave the rest to you!

.