Z-Table Transform Cheat Sheet: Table of Laplace and Z-transforms

Table of Laplace and Z-transforms X(s) x(t) x(kT) or x(k) X(z) Kronecker delta So(k) 1. - - 1 k=0 1 0 k # 0 So(n-k) 2. - - 1 n=k z-K 0 n k k 1 1 3. - 1(t) 1(k) S 1-z-1 1 4. e-at e-akT s+a 1-e-dr Tz-1 5. s2 t kT (1 - z-1)2 2 6. t (kT)2 S3 (1-z-1) 6 7. t3 (kT)3 s4 (1-z-1) a 8. 1-e-at 1 - e-akT (1-e-a) s(s+a) b-a 9. e-at - e-br (e-aT -e-bT) (s+a)(s+b) 1 10. te-at kTe-akT (s+a)2 (1-e-d'z-1)2 S 1-(1+aT)e-T 11. (s+a)2 (1-at)e-an (1 - akT)e-akT 2 12. te-at (s+a) (kT)2e-akT (1-e-d'z-1)3 a2 13. at - 1 + akT - 1 + T s2(s+a) zis aT 14. s2+w2 sin at sin akT 1-2z-1 cos aT + z1 1-z-1 cos aT 15. cos at cos akT 1-2z-cos oT+z a 16. (s+a)2+w2 e-art e-akT sin wkT 1-2e-acoswTe2aT2 s+a 17. e-art e-akT cos akT (s+a)2 +w2 2e-aT-cos wT+e-2aT 18. - - ak 1-az-1 ak z-1 19. - - k=1,2,3, 1-az-1 2-1 20. - - kak-1 (1-az-1)2 21. - - kak-1 (1-az-1) 22. - - k3a-- (1-az-1)4 23. - - k4ak-1 (1-az-1) 24. - a cos k r 1+az-1 x(t)=0fort