ztrans - Maple Programming Help

ztrans

Z transform

 Calling Sequence ztrans(f, n, z)

Parameters

 f - expression n - name z - name

Description

 • The function ztrans finds the Z transformation of f(n) with respect to z. Formally,

$\mathrm{ztrans}\left(f\left(n\right),n,z\right)=\sum _{n=0}^{\mathrm{\infty }}\frac{f\left(n\right)}{{z}^{n}}$

 • ztrans recognizes and specially handles a large class of expressions, and only resorts to using the definition to calculate the transformation if the given expression has an unknown form. If the Z transform of the given expression cannot be found in a closed form, then the left-hand side of the formal definition is returned, rather than the right-hand side.
 • The functions referred to in the literature as Delta and Step may be simulated in this function as charfcn[0](...) and Heaviside(...), respectively.

Examples

 > $\mathrm{ztrans}\left(f\left(n+1\right),n,z\right)$
 ${z}{}{\mathrm{ztrans}}{}\left({f}{}\left({n}\right){,}{n}{,}{z}\right){-}{f}{}\left({0}\right){}{z}$ (1)
 > $\mathrm{ztrans}\left(\mathrm{sin}\left(\frac{\mathrm{π}t}{2}\right),t,z\right)$
 $\frac{{z}}{{{z}}^{{2}}{+}{1}}$ (2)
 > $\mathrm{ztrans}\left(\frac{{3}^{n}}{n!},n,w\right)$
 ${{ⅇ}}^{\frac{{3}}{{w}}}$ (3)
 > $\mathrm{ztrans}\left(\mathrm{β}{5}^{n}\left({n}^{2}+3n+1\right),n,z\right)$
 ${\mathrm{β}}{}\left(\frac{{1}}{{5}}{}\frac{{z}{}\left(\frac{{1}}{{5}}{}{z}{+}{1}\right)}{{\left(\frac{{1}}{{5}}{}{z}{-}{1}\right)}^{{3}}}{+}\frac{{3}}{{5}}{}\frac{{z}}{{\left(\frac{{1}}{{5}}{}{z}{-}{1}\right)}^{{2}}}{+}\frac{{1}}{{5}}{}\frac{{z}}{\frac{{1}}{{5}}{}{z}{-}{1}}\right)$ (4)
 > $\mathrm{ztrans}\left(\mathrm{charfcn}[5]\left(t\right)\mathrm{Ψ}\left(t\right),t,w\right)$
 $\frac{\frac{{25}}{{12}}{-}{\mathrm{γ}}}{{{w}}^{{5}}}$ (5)
 > $\mathrm{ztrans}\left(n\mathrm{Heaviside}\left(n-3\right),n,z\right)$
 $\frac{{3}{}{z}{-}{2}}{{{z}}^{{2}}{}{\left({z}{-}{1}\right)}^{{2}}}$ (6)
 > $\mathrm{ztrans}\left(\mathrm{invztrans}\left(f\left(z\right),z,n\right),n,z\right)$
 ${f}{}\left({z}\right)$ (7)