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FIR Filter

  1. Nov 3, 2013 #1
    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

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


    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. jcsd
  3. Nov 4, 2013 #2

    collinsmark

    User Avatar
    Homework Helper
    Gold Member

    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.
    [tex]
    u[n] =
    \begin{cases}
    1 & \text{if } n \geq 0 \\
    0 & \text{if } n < 0
    \end{cases}
    [/tex]

    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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