Table of Z-Transforms

Table of Z-Transforms#

	f[n]	F(z).	Region of Convergence
1.	\(\displaystyle{\delta[n]}\)	\(\displaystyle{1}\)
2	\(\displaystyle{\delta[n-m]}\)	\(\displaystyle{z^{-m}}\)
3	\(\displaystyle{a^nu_0[n]}\)	\(\displaystyle{\frac{z}{z-a}}\)	\(\mid z \mid > a\)
4	\(\displaystyle{u_0[n]}\)	\(\displaystyle{\frac{z}{z-1}}\)	\(\mid z \mid > 1\)
5	\(\displaystyle{(e^{-anT_s})u_0[n]}\)	\(\displaystyle{\frac{z}{z-e^{-aT_s}}}\)	\(\displaystyle{\mid e^{-aT_s}z^{-1} \mid < 1}\)
6	\(\displaystyle{(\cos naT_s)u_0[n]}\)	\(\displaystyle{\frac{z^2 - z\cos aT_s}{z^2 -2z\cos aT_s + 1}}\)	\({ \mid z \mid> 1}\)
7	\(\displaystyle{(\sin naT_s)u_0[n]}\)	\(\displaystyle{\frac{z\sin aT_s}{z^2 -2z\cos aT_s + 1}}\)	\({\mid z \mid > 1}\)
8	\(\displaystyle{(a^n\cos naT_s)u_0[n]}\)	\(\displaystyle{\frac{z^2 - az\cos aT_s}{z^2 -2az\cos aT_s + a^2}}\)	\({\mid z \mid > 1}\)
9	\(\displaystyle{(a^n\sin naT_s)u_0[n]}\)	\(\displaystyle{\frac{az\sin aT_s}{z^2 -2az\cos aT_s + a^2}}\)	\({\mid z \mid > 1}\)
10	\(\displaystyle{u_0[n]-u_0[n-m]}\)	\(\displaystyle{\frac{z^m-1}{z^{m-1}(z-1)}}\)
11	\(\displaystyle{nu_0[n]}\)	\(\displaystyle{\frac{z}{(z-1)^2}}\)
12	\(\displaystyle{n^2u_0[n]}\)	\(\displaystyle{\frac{z(z+1)}{(z-1)^3}}\)
13	\(\displaystyle{[n+1]u_0[n]}\)	\(\displaystyle{\frac{z^2}{(z-1)^2}}\)
14	\(\displaystyle{a^n n u_0[n]}\)	\(\displaystyle{\frac{az}{(z-a)^2}}\)
15	\(\displaystyle{a^n n^2 u_0[n]}\)	\(\displaystyle{\frac{az(z+a)}{(z-a)^3}}\)
16	\(\displaystyle{a^n n[n+1] u_0[n]}\)	\(\displaystyle{\frac{2az^2}{(z-a)^3}}\)