|
信号,x[n] |
Z 变换,X(z) |
收敛域 |
1 |
δ[n] |
1 |
所有 z
|
2 |
δ[n - n0] |
z-n0 |
z ≠ 0
|
3 |
u[n] |
1 / (1 - z-1) |
|z| > 1
|
4 |
-u[-n - 1] |
1 / (1 - z-1) |
|z| < 1
|
5 |
nu[n] |
z-1 / (1 - z-1)2
|
|z| > 1
|
6 |
![{\displaystyle -nu[-n-1]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b9c7bfd00539cf805ba91e15a60b73576194dbd1) |
z-1 / (1 - z-1)2
|
|z| < 1
|
7 |
![{\displaystyle n^{2}u[n]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/556ff0a974378872385484fbeadf8bee8da04e97) |
 |
|z| > 1
|
8 |
![{\displaystyle -n^{2}u[-n-1]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bcc9d247970a92c7c6a69da9b5a272190dadcd24) |
 |
|z| < 1
|
9 |
![{\displaystyle n^{3}u[n]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0458b9d3eaa2c032ea05c85f0b2dc59809e61815) |
 |
|z| > 1
|
10 |
![{\displaystyle -n^{3}u[-n-1]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f66cd02f765990cd569d2cc47dd44cc75bfad0a3) |
 |
|z| < 1
|
11 |
![{\displaystyle a^{n}u[n]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ec08f4507612bf171a306727ec543e8b22909a8b) |
 |
|
12 |
![{\displaystyle -a^{n}u[-n-1]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cf8f7594a9aa188a37767ad6cbbcd1c932f5408c) |
 |
|
13 |
![{\displaystyle na^{n}u[n]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e0b15d6e4309b253c58fdf105b270217869762ad) |
 |
|
14 |
![{\displaystyle -na^{n}u[-n-1]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4a7df946d3646eb5c94313eb414edf4c9070d782) |
 |
|
15 |
![{\displaystyle n^{2}a^{n}u[n]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0dc9a83f632b9781ec66653e486b9f77fafe3bb0) |
 |
|
16 |
![{\displaystyle -n^{2}a^{n}u[-n-1]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d85083b09d1b7c73d32bdfcc120bd85c56504b66) |
 |
|
17 |
![{\displaystyle \cos(\omega _{0}n)u[n]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/07538580111cb3bee33a686fa3970039105fee57) |
 |
|z| > 1
|
18 |
![{\displaystyle \sin(\omega _{0}n)u[n]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d0a4e25fc75ace79158f75ab06339a9b87ce3665) |
 |
|z| > 1
|
19 |
![{\displaystyle a^{n}\cos(\omega _{0}n)u[n]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1a451552ec134261501b282063fca173b531a0ba) |
 |
|
20 |
![{\displaystyle a^{n}\sin(\omega _{0}n)u[n]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ee7ec057f4c8c7c307f3a58a9091e6e03d91f01d) |
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