iztrans

Inverse Z-Transform of Symbolic Expression

Compute the inverse Z-transform of 2*z/(z-2)^2. By default, the inverse transform is in terms of n.

syms z
F = 2*z/(z-2)^2;
iztrans(F)

ans =
2^n + 2^n*(n - 1)

Specify Independent Variable and Transformation Variable

Compute the inverse Z-transform of 1/(a*z). By default, the independent and transformation variables are z and n, respectively.

syms z a
F = 1/(a*z);
iztrans(F)

ans =
kroneckerDelta(n - 1, 0)/a

syms m
iztrans(F,m)

ans =
kroneckerDelta(m - 1, 0)/a

iztrans(F,a,m)

ans =
kroneckerDelta(m - 1, 0)/z

Inverse Z-Transforms Involving Kronecker Delta Function

Compute the inverse Z-transforms of these expressions. The results involve the Kronecker Delta function.

syms n z
iztrans(1/z,z,n)

ans =
kroneckerDelta(n - 1, 0)

f = (z^3 + 3*z^2)/z^5;
iztrans(f,z,n)

ans =
kroneckerDelta(n - 2, 0) + 3*kroneckerDelta(n - 3, 0)

Inverse Z-Transform of Array Inputs

Find the inverse Z-transform of the matrix M. Specify the independent and transformation variables for each matrix entry by using matrices of the same size. When the arguments are nonscalars, iztrans acts on them element-wise.

syms a b c d w x y z
M = [exp(x) 1; sin(y) i*z];
vars = [w x; y z];
transVars = [a b; c d];
iztrans(M,vars,transVars)

ans =
[ exp(x)*kroneckerDelta(a, 0), kroneckerDelta(b, 0)]
[       iztrans(sin(y), y, c),   iztrans(z, z, d)*1i]

If iztrans is called with both scalar and nonscalar arguments, then it expands the scalars to match the nonscalars by using scalar expansion. Nonscalar arguments must be the same size.

syms w x y z a b c d
iztrans(x,vars,transVars)

ans =
[ x*kroneckerDelta(a, 0),       iztrans(x, x, b)]
[ x*kroneckerDelta(c, 0), x*kroneckerDelta(d, 0)]

Inverse Z-Transform of Symbolic Function

Compute the Inverse Z-transform of symbolic functions. When the first argument contains symbolic functions, then the second argument must be a scalar.

syms f1(x) f2(x) a b
f1(x) = exp(x);
f2(x) = x;
iztrans([f1, f2],x,[a, b])

ans =
[ iztrans(exp(x), x, a), iztrans(x, x, b)]

If Inverse Z-Transform Cannot Be Found

If iztrans cannot compute the inverse transform, it returns an unevaluated call.

syms F(z) n
F(z) = exp(z);
f = iztrans(F,z,n)

f =
iztrans(exp(z), z, n)

Return the original expression by using ztrans.

ztrans(f,n,z)

ans =
exp(z)