Basic “filtering” in digital communications

I am completely stuck on solving some problems for my digital communications class. Junior level undergrad class, so fairly basic. I have been searching around all day for related articles etc but can't seem to find any that are helpful. Any help would be much appreciated. Here are the three questions:

For the coefficients my initial hunch is just to make c2 and c3 = 0, which would leave $\hat{y}[1] = y[1]$. My other attempt is to create a system of equations so the $x[2]$ terms are cancelled and the $x[1]$ terms are the only ones left over, but this system proves difficult to me and I am left with a mess of noise. For some reason I can only get two equations with three unknowns.

$$c_3= -3 c_2 \\ c_1 + \frac13 c_2 + \frac14 c_3 = 1$$ where $c_1,c_2,c_3$ are constants.

Sorry for my terrible formatting. I believe I completed the first question correctly, here was my process.

Moving on to question 2, for part A I'm fairly sure it is what I was attempting to do before so I got c3=-3 * c2

for part b, I am stuck again because my brain keeps going back to the idea that I should just make c2 and c3 both 0, because it appears to me our goal is to make x1 recoverable.

• I'm voting to close this question as off-topic because it is a homework question with no demonstrated attempt at a solution. – Matt Young Mar 31 '15 at 3:44
• I understand your point, but I don't really understand the question so any "attempt" I make won't even be in the right direction. If you could at least give me a hint as to how to get started (assuming you know how to do it), I would be very appreciative. Thanks – Kevin Dahm Mar 31 '15 at 3:53
• @KevinDahm any attempt so long as its reasonable will help members of this site guide you. They may not just tell you answer. There is value in discovering the answer yourself. I suggest you your chapter on this topic, and then TRY to answer. Who cares if its wrong. Do what you THINK is the correct way. Give some explanation why you are doing certain things. When you have put some effort, members of this site will spend their time to help you. – efox29 Mar 31 '15 at 4:04
• Alright, sorry I'm new here. I edited the question to include my naive attempts to question 1, part a. – Kevin Dahm Mar 31 '15 at 4:09
• Just to complete the record, this instructor of ECE 361 at the University of Illinois at Urbana-Champaign confirmed that this question is from homework assigned in the course. The homework submission deadline has passed and so if anyone wants to take a whack at it, at least the OP will not be getting an unfair advantage over his fellow-students – Dilip Sarwate Apr 4 '15 at 3:39