Heaviside step function, signal and systems

[Jncik]

Homework Statement

given this discrete time signal

x[n] = u[n] - u[n-6]

find for which n the even part of x is 0

The Attempt at a Solution

the even part is

x' = 1/2(x[n] + x[-n]) = 1/2(u[n] - u[n-6] + u[-n] - u[6-n])

now i find that

u[n] + u[-n] is 2 for n = 0 and 1 for n != 0
u[n-6] + u[6-n] is 2 for n = 6 and 1 for n!=6

let z[n] = u[n] + u[-n]
k[n] = u[n-6] + u[6-n]

we want to find where 1/2 * (z[n] - k[n]) = 0 => z[n] - k[n] = 0

this is
0 for n != 0 and n!=6
1 for n = 0
-1 for n = 6

is this correct? I am new to this thing.. if you can please help me :)

 

[diazona]

Your reasoning makes sense to me... is there some reason you suspect that your answer is wrong?

 

[Jncik]

Your reasoning makes sense to me... is there some reason you suspect that your answer is wrong?

No not really, I just wasn't 100% sure for my answer, my book didnt really have any answers and i needed to know if i understood these simple concepts.. thanks for your help now I can move on :)