Symbolic Math Toolbox™

ztrans - z-transform

Syntax

F = ztrans(f) F = ztrans(f,w) F = ztrans(f,k,w)

F = ztrans(f) is the z-transform of the scalar symbol f with default independent variable n. The default return is a function of z.

The z-transform of f is defined as

where n is f's symbolic variable as determined by findsym. If f = f(z), then ztrans(f) returns a function of w.

F = F(w)

F = ztrans(f,w) makes F a function of the symbol w instead of the default z.

F = ztrans(f,k,w) takes f to be a function of the symbolic variable k.

Z-Transform	MATLAB Operation
f(n) = n⁴	`syms n` `f = n^4` `ztrans(f)` returns `(z^4 + 11z^3 + 11z^2 + z)/(z - 1)^5`
g(z) = a^z	`g = a^z` `ztrans(g)` returns `-w/(a - w)`
f(n) = sin(an)	`f = sin(an)` `ztrans(f,w)` returns `(wsin(a))/(w^2 - 2cos(a)w + 1)`

Z-Transform

MATLAB Operation

f(n) = n⁴