# Step response of a LTI system

## Homework Statement

Calculate the step response of the system (i.e. response to x(n) = u(n)

Previously calculated the impulse response becomes h(n) 3/11 $(5/8)^{n}$ u(n) + 5/22$(1/8)^{n}$u(n)

## Homework Equations

H(z) =$\frac{Y(z)}{X(z)}$

u(n) =$\frac{1}{1-z^{-1}}$

## The Attempt at a Solution

Convolution seems a possible way but that would involve an insane amount of maths. But convolution is multiplication in the z domain. Transforming the impulse response back we get
H(z)=3/11 $\frac{1}{1-\frac5 8z^{-1}}$ + 5/22$\frac{1}{1-\frac1 8z^{-1}}$

Then take from the other side x(z) and multiple the top halves by X(z).

After that switch x(z) for the u(n). After doing that it becomes something incredibly stupid that i actually cant manage to write it on this! Any help would be appreciated!