# Impulse Response In A Discrete System

Hey guys, this is my first post and I'm looking for a bit of help

This is going to sound really easy (and I know it is) but I can't for the life of me remember how to work out the Impulse Response Function of this system. I've tried google for a few hours but nowhere that gives it in laymans terms.

What I would like to know is what the impulse response function h(n) is of System A

y(n) =$$\frac{x(n) - 2x(n-1) + x(n-2)}{2}$$

Any assistance would be great, It doesn't even need to be the answer just how I can work it out.

Thanks

## Answers and Replies

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An impulse is 1 for n = 0 and 0 for any other n.
Start with n = 0. How much is y(0)?
Then make n = 1, 2, 3,... and calculate y(n). After a certain n, y(n) will be always zero.

Take the Z transform of it. So,

Y(z)= X(z)/2 -2/2X(z)z^(-1) +X(z)/2(z^-2)and so on. Then you'll get a transfer function H(z)= Y(z)/X(z)

the Z.T. of an impulse can be found (look up the table, it is =1) then you find the inverse Z. T. to get y[n]

I think (you need to check it) Y(Z)= 0.5 + z^-1 + 0.5z^-2