HELP unit-pulse response for the discrete time system problem

[Raihan]

HELP!unit-pulse response for the discrete time system problem

Please help me solve these problems. Thank you so much for all your help.

Compute the unit-pulse response for the discrete time system

1) y[n + 2] + 1/2 y[n+1]+1/4y[n] = x[n+1]-x[n] (for n = 0, 1, 2)
For number 1) the options for right answers are:
a. 0, -1, 2
b. 0, -1, 1/2
c. 0, 1, -3/2
d. 0, 1, 2

2) y[n + 2] + 1/4 y[n+1]-3/8y[n+2] = 2x[n+2]-3x[n](for n = 0, 1, 2)
For number 2) the options for right answers are:
a. 0, -1, 4
b. 2, -1/4, 1/2
c. 0, -1, -3/2
d. 2, -1/2, -17/8

I am completely stuck if you could at least give me the right answer still it will be helpful.

 

[berkeman]

Do not double-post, Raihan. The other thread you started with the same question is in the EE forum:

https://www.physicsforums.com/showthread.php?t=138742

This thread is now locked. Any responses you receive will need to be in the other thread. And remember that you need to show your own work in order to get help her in the PF homework forums. We can be a big help if you are willing to do some work. We are not a source of answers to your homework problems.

 

[piercas]

I am happy to assist with your problem. The unit-pulse response for a discrete time system is the output of the system when the input is a unit impulse function, also known as a Kronecker delta function. This means that the input is a single value of 1 at time n=0 and 0 at all other times.

To solve the first problem, we can use the given equation and substitute in the input of x[n]=1 at n=0 and x[n]=0 at all other times. This results in the following equation:

y[n+2] + 1/2 y[n+1] + 1/4 y[n] = 1-0 = 1

We can then solve for y[n] by setting n=0:

y[2] + 1/2 y[1] + 1/4 y[0] = 1

Next, we can set n=1 and solve for y[n+1]:

y[3] + 1/2 y[2] + 1/4 y[1] = 0

Finally, we can set n=2 and solve for y[n+2]:

y[4] + 1/2 y[3] + 1/4 y[2] = 0

We now have a system of three equations with three unknowns (y[0], y[1], y[2]). Solving this system of equations will give us the unit-pulse response for the discrete time system.

Based on the options given, the correct answer for the first problem is option c. 0, 1, -3/2.

For the second problem, we can follow the same process of substituting in the unit impulse function and solving for y[n]. The resulting system of equations is:

y[n+2] + 1/4 y[n+1] - 3/8 y[n] = 2-0 = 2

y[n+3] + 1/4 y[n+2] - 3/8 y[n+1] = 0

y[n+4] + 1/4 y[n+3] - 3/8 y[n+2] = -3

Again, solving this system of equations will give us the unit-pulse response for the discrete time system. Based on the options given, the correct