# Impulse Response

## Homework Statement

I have an impulse response h(n)=e^(0.1n)*[u(n)-u(n-8)] and an input x(n)={0,1,2,3,0}, how do I find the output y(k)?
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## The Attempt at a Solution

i don't even know how to solve. should i try convolution or should i substitute the values of x(n) in h(n). and idk why its y(k) instead of y(n) you don't need to put the exact solution. you just need to explain what i need to do. thanks :)[/B]

## Answers and Replies

For a discrete time LTI (Linear Time Inviariant) system, the output is completely determined by the output and the impulse response, wich is the response to an impulse funtion (often called delta function). d[n] with d =1 and d[x] = 0 if x<>0.
if you know the response to d[n], you know the response to d[n-t], and any input signal is a linear combination of impulse functions with different time shifts.
The way to determine this is the convolution sum. See here for example:
http://www.eecg.toronto.edu/~ahouse/mirror/engi7824/course_notes_7824_part6.pdf

For a discrete time LTI (Linear Time Inviariant) system, the output is completely determined by the output and the impulse response, wich is the response to an impulse funtion (often called delta function). d[n] with d =1 and d[x] = 0 if x<>0.
if you know the response to d[n], you know the response to d[n-t], and any input signal is a linear combination of impulse functions with different time shifts.
The way to determine this is the convolution sum. See here for example:
http://www.eecg.toronto.edu/~ahouse/mirror/engi7824/course_notes_7824_part6.pdf

Thanks for your response!
So i just need to convolve x(n) and h(n)? and the answer is y(n)? how will it become y(k) tho?

So i just need to convolve x(n) and h(n)? and the answer is y(n)? how will it become y(k) tho
Sorry, I have no idea why they use y[k] and not y[n].