`ztrans`

Z-transform of a symbolic sequence.

Syntax

F = ztrans(f)

Transforms f in its default index, returning a function of z.

F = ztrans(f, n, z)

Transforms f(n) to F(z) using the stated variables.

Description

The Z-transform of a sequence f(n) is the sum of f(n) z^(-n) for n from 0 to infinity. ztrans returns the closed form, for example z/(z - a) for a^n. It is the discrete counterpart of laplace, and iztrans inverts it.

Input arguments

f: Symbolic expression, function or sequence in the index n.
n: Index variable (discrete time).
z: Transform variable.

Output arguments

F: Symbolic expression in z.

Example

Geometric and ramp sequences

syms n z
ztrans(2^n, n, z)
ztrans(n, n, z)

Output

ans = z/(z - 2)
ans = z/(z - 1)^2

Notes

MatLivre covers the common transform pairs (polynomials, exponentials, sines and cosines, Dirac and Heaviside); other inputs stay unevaluated even when MATLAB finds a closed form.

ztrans