I have a function$1. Sep 23, 2011 vaibhavtewari I have a function [itex] \displaystyle\sum_{n=0}^{N-1}\left(x_n-\sum_{i=0}^{L-1}a_iS_{i+n}\right)^2$

if I do a partial differentiation with respect to $S_k$ what would I get ?

thanks

2. Sep 23, 2011

CompuChip

Re: differentiation

Will it help you if I note that you can write it as
$$\sum_{n = 0}^{N - 1} (C - a_{k - n} S_k)^2$$
where C is a constant with respect to Sk.

3. Sep 23, 2011

vaibhavtewari

Re: differentiation

variable S_k is not a constant, so there are basically N+L variables...thanks for trying

4. Sep 23, 2011

CompuChip

Re: differentiation

I assume that you only differentiate with respect to one value of k at the time?

5. Sep 23, 2011

vaibhavtewari

Re: differentiation

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