[Robert Orban]

In article om,
says...



The advantage of a digital filter is that you CAN build a filter
that has exactly the same frequency and phase characteristics
of an equivalent analog filter. And an added advantage is that
you can build filters that don't, if needed.

I would modify this statement as follows:

The advantage of a digital filter is that you CAN build a filter that
approximates the frequency and phase characteristics of an equivalent analog
filter to whatever accuracy you desire, provided that you allow addition of
an arbitrary pure delay to the filter. Strictly speaking, the added delay
causes the phase response of the digital filter to be very different from
the phase shift of the analog filter, although this is an academic argument
for most purposes(however not for live sound, sound for picture, and a
significant number of other real-world applications).

If you demand that your digital filter be minimum phase, then the digital
filter can never have exactly the same magnitude and phase response as the
prototype analog filter you are trying to duplicate. The differences will
often be quite large, particulaly as you approach Nyquist. The common
transforms (bilinear, matched-z, impulse-invariant, and step-invariant) all
have errors of some sort.

Regarding the main subject of this thread, IIR subsonic digital filters are
a challenge to implement correctly because they have high noise gain.
Highest performance requires choosing a low-noise structure and also making
sure that the finite word length arithmetic that implements the filters has
a sufficient number of bits. There is are a lot of research papers on this
subject.