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I have a function[itex]

  1. Sep 23, 2011 #1
    I have a function

    [itex] \displaystyle\sum_{n=0}^{N-1}\left(x_n-\sum_{i=0}^{L-1}a_iS_{i+n}\right)^2[/itex]

    if I do a partial differentiation with respect to [itex]S_k[/itex] what would I get ?

    thanks
     
  2. jcsd
  3. Sep 23, 2011 #2

    CompuChip

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    Re: differentiation

    Will it help you if I note that you can write it as
    [tex]\sum_{n = 0}^{N - 1} (C - a_{k - n} S_k)^2[/tex]
    where C is a constant with respect to Sk.
     
  4. Sep 23, 2011 #3
    Re: differentiation

    variable S_k is not a constant, so there are basically N+L variables...thanks for trying
     
  5. Sep 23, 2011 #4

    CompuChip

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    Re: differentiation

    I assume that you only differentiate with respect to one value of k at the time?
     
  6. Sep 23, 2011 #5
    Re: differentiation

    that is true but then I solve these simultaneous equations...so I was hoping for something structured..
     
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