Determine the unit-step response of the discrete-time LTI systems

[Mr.Tibbs]

Determine the unit-step response of the discrete-time LTI
systems described by the following impulse responses:

h[n]=(0.9)^{n}e^{j(\pi/2)n}u[n]So I am completely confused. . . I don't even know how to start. . . I want to say that I need to do a summation but the more examples and text I look up the more I'm in the dark. . . any help is appreciated.

The only thing I can think to start is you assume

x[n] = u[n]

 

[rude man]

How about convolving u[n] with your h[n]?

 

[Mr.Tibbs]

My apologies for taking so long to reply. I was able to talk to my professor and this is what I have now.

\sum(0.9)^{k}e^{j(\pi/2)k}u[n-k] from k = -∞ to ∞.

this turns into

\sum(0.9)^{k}e^{j(\pi/2)k} from k = 0 to n.

using the property of summation :

\sum a^{k} = \frac{1-a^{n+1}}{1-a}

my new snag is what do I define as a?