There is only one common method to estimate interpolated peaks in DSP.
What is done in this method is to compute values for the \"perfectly
bandlimited signal\" which passes through the sample points. This
entails designing an approximation to a perfect brick-wall filter.
The ideal brick-wall filter takes infinite computational power to
implement, which is why an approximation must be used. The
problem with the approximation is that, no matter how much
DSP is used to do the approximation, there is no way to
guarantee that the error between the peak estimate and the
actual bandlimited peak value is finite. In other words, the
error in the peak estimate can always be unbounded, no matter
how good the approximation is on the brick-wall filter.
Another problem is that there are no D/A converters that have
perfect \"reconstruction filters\". Therefore, the peak level of the
analog signal produced by the D/A will not be the same as
the peak level for the perfectly bandlimited signal. Different
D/A converters will have different filters, which will produce
different analog peak levels, for the same digital signal.
Finally, the biggest differences between interpolated peak levels
and peak sample values occur during transients. Human beings
are not very perceptive of distortion that lasts less than 4-5 mS,
so that an occasional transient which is mangled by a poor D/A
may not even be perceived. This explains the popularity of limiters
with very fast attack and release settings to take one or two dB
off transients. The reason these limiters are \"transparent\" is not
because they are not limiting very much ; it is because the time
over which the gain is reduced is very short, since only transients
reach the top one or two dB of the original signal.
To summarize: Interpolated peak estimation as currently known in the
DSP community is an approximation, with unbounded error, which
estimates something that may not resemble what comes out of
our D/A converters.