ztrans (Symbolic Math Toolbox)

z-transform

Syntax

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

Description

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 = 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.

Examples

Z-Transform
MATLAB Operation

f = n^4

ztrans(f)
returns

z*(z^3+11*z^2+11*z+1)/(z-1)^5

g = a^z

simplify(ztrans(g))
returns

-w/(-w+a)

f = sin(a*n)

ztrans(f,w)
returns

w*sin(a)/(w^2-2*w*cos(a)+1)

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

See Also

fourier, iztrans, laplace

zeta Compatibility Guide