Unit-Pulse Response for Discrete Time System

  • Thread starter hoser1000
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  • #1
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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[0]=2*1-y[1]<-----This is where I am getting confused. Doesn't y[1] 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!!
 

Answers and Replies

  • #2
CEL
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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[0]=2*1-y[1]<-----This is where I am getting confused. Doesn't y[1] 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] = 0.
Now substitute x[n] by the impulse function and solve iteratively for y[1], y[2], y[3].
 
  • #3
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Why don't you use Z transforms. That'll provide you with some more insight.
 
  • #4
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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
 
  • #5
CEL
656
0
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
The reasoning is the same. Start with n = -1.
x[n] = x[-1] = 0
x[n+1] = x[0] = 1
x[n+2] = x[n+3] = ... = 0
y[n] = y[-1] = 0
y[n+1] = y[0] = 0
....
Or, as unplebeian suggested, use the z-transform
 

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