# Unit-Pulse Response for Discrete Time System

The question is: Compute the unit-impulse response h[n] for n=0,1,2,3 for each of the following discrete-time systems.

Equation:
y[n+1] + y[n] = 2x[n]

I am trying to figure out how to solve this equation. I understand the example in the book but I don't understand what to do when it calls a future value (n+1)

I rewrote the equation as:
y[n]=2delta[n]-y[n+1]

When n=0 delta[n] is 1 so:
y=2*1-y<-----This is where I am getting confused. Doesn't y refer to my answer when I use the value n=1? How can I get a solution if each equation will refer to the next future equation? The example in the book uses y[n-1] so for each value of n it refers to the previous answer for y[n].

Any help would be much appreciated!!

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CEL
The question is: Compute the unit-impulse response h[n] for n=0,1,2,3 for each of the following discrete-time systems.

Equation:
y[n+1] + y[n] = 2x[n]

I am trying to figure out how to solve this equation. I understand the example in the book but I don't understand what to do when it calls a future value (n+1)

I rewrote the equation as:
y[n]=2delta[n]-y[n+1]

When n=0 delta[n] is 1 so:
y=2*1-y<-----This is where I am getting confused. Doesn't y refer to my answer when I use the value n=1? How can I get a solution if each equation will refer to the next future equation? The example in the book uses y[n-1] so for each value of n it refers to the previous answer for y[n].

Any help would be much appreciated!!
It is exactly the contrary of what you did. You should write y[n+1] as a function of y[n] and x[n].
By definition, the impulse response of a system is the zero state response of that system when the input is an impulse, so you have y = 0.
Now substitute x[n] by the impulse function and solve iteratively for y, y, y.

Why don't you use Z transforms. That'll provide you with some more insight.

Hey,

Does this same reasoning apply if the equation is:

y[n+2] + y[n+1] + y[n] = x[n+1] - x[n]

if so, i too am lost.

is there another way to describe it?
or could you just go through it step by step

CEL
Hey,

Does this same reasoning apply if the equation is:

y[n+2] + y[n+1] + y[n] = x[n+1] - x[n]

if so, i too am lost.

is there another way to describe it?
or could you just go through it step by step