🚀 go-pugleaf

Hewlett-Packard sells an instrument that has the capability you want
built-in.  It's called an HP 3563A Control Systems Analyzer.  The
analyzer has two analog inputs (100kHz) two digital inputs (256 ksamples
per sec),  an analog source and a digital source.   It also has two
curve-fitters, one for the s-domain and one for the z-domain.  

For your application, the z-domain curve-fitter would be applied to a
frequency response data which was measured using the analog inputs or 
or synthesized using an s-domain model (e.g. poles/zeros).  The curve-
fitter produces a pole-zero model which can be easily translated into
a difference equation for use in a digital filter.  Unlike the usual s->z 
transforms such as the bilinear, impulse-invarient, or step-invarient 
methods (which are also available in the analyzer), the curve-fitter can 
be made to use any specified filter topology.  For example, an N pole 
analog filter can be approximated by an M tap FIR or IIR filter where 
M is not a function of N.   

Another advantage of using curve-fitting is that a weighting function can 
be used to emphasise areas of the the frequency response function for which 
a close approximation is important.  This is similar to pre-warping with 
the bi-linear transform except that it's not limited to a single frequency 
point. It's also possible, before curve-fitting, to pre-distort the frequency
response data to account for things like the sin(x)/x rolloff that will
occur if the analog signal is reconstructed using a D/A converter.

The only dissadvantage of using the curve-fitting approach to get from s->z, 
as compared to a method like the bi-linear transform, is that, for IIR 
filters, the curve-fitter doesn't always produce a z-domain model which 
is stable.  Usually when this happens, the sample rate and/or the filter 
order is too low.


					Bob Cutler
                                        KE7ZJ
					Hewlett-Packard
					Lake Stevens Instrument Division
					Everett, WA 98205.