Transforms of some useful sequences

(1) The unit sample δ(n):

(2) Unit step u(n) (for positive time):

(3) Unit step -u(-n-1) (for negative time):

(4) Exponential a nu(n) , derived in previous example:

(5) Exponential - bnu(-n -1) ; negative time; derived previous:

(6) Unit ramp n u(n). Given that ?[u(n)] = U(z) =z/z-1

(7) Sinusoid sin w₀ n u(n) : ?{sin w₀ nu(n)}= 

Using the identities

we have

 An extaention using proprty 3

(8) Cosinusoid cos w₀n u(n) . Using the relation 

that for sinusoid we get

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