# Find $Y(\omega)$ as a function of $X(\omega)$ [closed]

I have a question regarding my homework.

Let's assume that the transform of $x[n]$ is $X(\omega)$.

1. Find $Y(\omega)$ as a function of $X(\omega)$: $$y[n] =\cases{x[n/2],&\text{if } n \text{ is even}\cr 0,&\text{if } n \text{ is odd}}$$
2. Find $Z(\omega)$ as a function of $X(\omega)$: $$z[n] =\cases{x[n/2],&\text{if } n \text{ is even}\cr x[(n-1)/2],&\text{if } n \text{ is odd}}$$
• Since this is homewrok, what have you done yourself to try and solve the problems? Can you write down what $X(\omega)$ is and how it relates to $x[n]$? Ditto for $Y(\omega)$ and $y[n]$. – Dilip Sarwate Jan 31 '12 at 21:58
• Hint: $y[n]$ looks like $x[n]$ with zeros inserted between every other sample. If you look closely, $z[n]$ is very similar to $y[n]$, but inserted between samples are not zeros, but copies of previous sample. What do these two things do to your spectrum? I suggest trying to come up with a signal and steming what results look like in MATLAB. – Phonon Jan 31 '12 at 22:55
• This types of problems is intended as a practice to apply basic properties of the DFT. They can all be broken down into basic operations like scaling, shifting, stretching, adding, multiplying, convolving etc. What you need to do is break down the problems into the individual basic steps and apply them one by one in the right sequence. One hint: You need to solve the first one first. It's just one extra step to the second. Good luck. Here is one example of how that works dsp.stackexchange.com/questions/1136/… – Hilmar Feb 1 '12 at 13:52
• I have tired during the last hours to come to a solution but not worked out for me. If someone could please upload the answer i will be greatful, because the due date is in 5 hours from now. Thanks for all your kind help !!! – Danny Lavsky Feb 1 '12 at 17:44