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Signal Processing

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  • $\begingroup$ Does it have to follow $ y[n] = \alpha x[n] + (1 - \alpha) y[n - 1] $ precisely]? $\endgroup$ Commented Oct 6, 2011 at 13:32
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    $\begingroup$ This is bound to become a very poor approximation. Can't you afford anything more than a first-order IIR? $\endgroup$ Commented Oct 6, 2011 at 13:42
  • $\begingroup$ You might want to edit your question so that you don't use $y[n]$ to mean two different things, e.g. the second displayed equation could read $z[n] = \frac{1}{k}x[n] + \cdots + \frac{1}{k}x[n-k+1]$, and you might want to say what exactly is your criterion of "as good as possible" e.g. do you want $\vert y[n] - z[n]\vert$ to be as small as possible for all $n$, or $\vert y[n] - z[n]\vert^2$ to be as small as possible for all $n$. $\endgroup$ Commented Oct 6, 2011 at 13:45
  • $\begingroup$ @Phonon, yes, it must be a first order IIR. The criteria is simple, the result $ y[n] $ should be as close as possible to the mean of the last $ k $ inputs to the system where $ n \in [k, \inf] $. I would be happy to see the result for both cases. Though I assume analytic solution is only viable for $ {|y[n]−z[n]|}^{2} $. $\endgroup$ Commented Oct 6, 2011 at 13:53