In practice, measurements are never perfect. Let denote the measured output signal, where is a vector of ``measurement noise'' samples. Then we have

It is also straightforward to introduce a *weighting function* in
the least-squares estimate for
by replacing
in the
derivations above by
, where is any positive definite
matrix (often taking to be diagonal and positive). In the present
context, (time-domain formulations), it is difficult to choose a
weighting function that corresponds well to *audio perception*.
Therefore, in audio applications, frequency-domain formulations are
generally more powerful for linear-time-invariant system
identification. A practical example is the frequency-domain
equation-error method described in §G.4.3 [75].

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