Multiplication par la variable d'évolution : n f(n) u(n)
modifier
Pour simplifier l'écriture j'ai écrit le signal f(n) au lieu du signal causale discret f(n) u(n).
Le signal f(n) Transformée en Z F(z) Z[n f(n)] = -z F'(z)
u(n) z/(z-1) -z [ z/(z-1) ]' = -z [-1/(z-1)^2]
n z/(z-1)^2 -z [ z/(z-1)^2 ]' = -z [-(z+1)/(z-1)^3]
n^2 z(z+1)/(z-1)^3 -z [ z(z+1)/(z-1)^3 ]' = -z [-(z^2+4z+1)/(z-1)^4]
a^n z/(z-a) -z [ z/(z-a) ]' = -z [-a/(z-a)^2]
cos(kn) [z^2-z cos(k)]/[z^2-2z cos(k)+1] -z [ [z^2-z cos(k)] / [z^2-2z cos(k)+1] ]' =
-z [2z-(z^2+1)cos(k)] / [z^2-2z cos(k)+1]^2
sin(kn) [z sin(k)]/[z^2-2z cos(k)+1] -z [ [z sin(k)] / [z^2-2z cos(k)+1] ]' =
-z [ -[(z^2-1)sin(k)] / [z^2-2z cos(k)+1]^2 ]
