# Impulse Response

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1. Apr 24, 2017

### maearnie

1. The problem statement, all variables and given/known data
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)?

2. Relevant equations

3. 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 :)

2. Apr 24, 2017

### willem2

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[0] =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

3. Apr 24, 2017

### maearnie

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

4. Apr 24, 2017

### willem2

Sorry, I have no idea why they use y[k] and not y[n].