Finding output eqn using DTFT and inverse DTFT knowing impulse and input eqns!

Hi,

The question is apparently simple, but I am very stuck and have been working on it for way too long, I must be missing something :(

Any help is greatly appreciated.

I am given an impulse response:

and input:

so to calculate

I know that:

and

so my strategy (and following the questions instructions) was to find then multiply it with to get and finally use the inverse DTFT to find .

so...

simplifying this summation...

similarly

Now, when I multiply these two together, I have no idea how to find the inverse DTFT.

I have got:

how can I find the DTFT of something like this? I don't know the period of it and I have no idea how to simplify it into something to apply the inverse DTFT which I know as:

http://upload.wikimedia.org/math/7/2...781d98321b.png

like I said, any advice would be greatly appreciated.

I have just found myself completely lost with this problem and doing loops trying to simplify my is absolutely killing me.

Thanks a lot!