# FIR Filter

1. Nov 3, 2013

### freezer

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

Consider the FIR filter with {bk} = {3, 4, -4, -3}. These are the filter coefficients for k = 0, 1, 2, and 3, respectively. Sketch the output y[n] where the input is:

x[n] = δ[n]
x[n] = (u[n] - u[n-2])
x[n] - u[n]

2. Relevant equations

$\sum^{M}_{k=0}b_k x[n-k]$

3. The attempt at a solution

I am not sure how to process this form.
I would build a table

for the first one x[0] = 3, x[2] = 4, etc..
for second x[0] = 3,..., x[3]=(3-4) = -1

I my notes don't have anything with u[n]

2. Nov 4, 2013

### collinsmark

That's the right idea, with the exception of: don't you mean " y[0] = 3, y[1] = 4. etc.."? (As opposed to x[0] = 3, x[2] = 4?)

I don't think that's quite right.

u[n] is the unit step function.
$$u[n] = \begin{cases} 1 & \text{if } n \geq 0 \\ 0 & \text{if } n < 0 \end{cases}$$

I suggest making a table giving u[n] as a function of n, for n = -1 to around 7 or so. Then do the same thing for -u[n-2]. Then again for u[n] - u[n-2]. And finally make another table for y[n] with that input.

Last edited: Nov 4, 2013
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