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As a follow-on to this question about estimating a transfer function of an unknown system using a Wiener filter,

  1. How would you put a minimum MSE criteria on how well the estimated filter weights matched the actual transfer function of the system? [Suppose you needed the MSE to be no more than -50dB]?

  2. How would you change his formulation if you wanted poles as well as zeroes (an IIR rather than an FIR filter)?

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  1. The desired MSE is application dependent, so there can be no general rule. If the approximation doesn't satisfy your needs you can increase the filter length to obtain a better match.
  2. There is no straightforward way to change the FIR Wiener filter solution to an IIR solution because the IIR formulation results in a set of nonlinear equations which have no closed-form solution. The IIR solution might also be unstable, so FIR filters are a much more practical choice when computing a Wiener filter.
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