ztrans (Symbolic Math Toolbox)

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

ztrans(g)
returns

-w/(-w+a)

f = sin(a*n)

ztrans(f,w)
returns

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

f = exp(k*n^2)*cos(k*n)

ztrans(f,k,x)
returns

x*(-exp(-n*2)*cos(n)+x)/
(-2*x*exp(-n^2)*cos(n) + x^2+
exp(-2*n^2))

Z-Transform	MATLAB Operation
	`f = n^4` `ztrans(f)` returns `z(z^3+11z^2+11*z+1)/(z-1)^5`
	`g = a^z` `ztrans(g)` returns `-w/(-w+a)`
	`f = sin(an)` `ztrans(f,w)` returns `sin(a)w/(1-w*cos(a)+w^2)`
	`f = exp(kn^2)cos(kn)` `ztrans(f,k,x)` returns `x(-exp(-n2)cos(n)+x)/` `(-2xexp(-n^2)cos(n) + x^2+` `exp(-2n^2))`

See Also
fourier, iztrans, laplace

zeta Compatibility Guide