Ok, this has been one of those phun/bizarre discussions - let's see if I can gather my thoughts and
produce a useful post. One of the main topics of this thread has been the "accuracy" of phase response
measurements. First off, we shall assume that we are actually measuring and not simply (if you can call
it simple) calculating the phase response based on the minimum phase of a measured frequency
response magnitude. I know that Smaart phase response is produced from an actual measurement of the
system under test. (Tom, is this what you meant with your comment, "some other measurement systems
don’t measure actual acoustic phase that I need."? - My apologies if I have miss-read/understood your
post.)
So, the next question is, what is the true/"actual"/accurate phase response. And more to the point of
this thread, what does that phase response trace look like? Well, that depends entirely upon the time
reference of your measurement - what have you chosen for your time-zero for your measurement? Just
as a image of an object will vary based on the angle from which it is viewed, the phase response trace
will look different depending upon the time reference chosen for the measurement. I guess, if we were
to be extremely literal with our phase measurements, we'd have to use the point where we have
obtained the reference signal for our measurement as our time-zero (e.g. the output of the console, the
input to the processor or amp) However, because the systems we are measuring almost always have
some excess/bulk/group delay (due to processor latency, signal delays, or propagation delays of sound
through air), we generally like to back that delay out of our measurement (since it causes a lot of
annoying wrapping in the phase trace) and simply try to isolate the phase response of the system of
interest - and we do this normally by adding some sort of measurement delay to our reference signal effectively moving the time-zero of our measurement to some later time of our own choosing. So much
of the discussion in this thread comes down to what point in time to use as our T-zero?
To take this discussion sideways a step, let's ask ourselves why we are interested in the phase response
of our system in the first place. One of the primary reasons for consulting the phase trace is to see the
relative time arrival of the energy at various frequencies passing through our system(s) - if it all came
through with the same delay, our phase traces would all be phlat (after backing out the group delay) and
this discussion wouldn't be any phun. SO, the idea is to see what energy is leading and what is lagging
(or in the case of causal system phase trace devotees, which energy is lagging, and which is lagging
more . . .) The important point here is that these measurements are all relative! There is no write or
rong. (assuming you are making your measurement correctly - doh!) If you are looking at x-over
timing, it is often desirable to re-time your measurement to the frequencies around x-over - just for a
clearer view. The important thing in gathering usable phase data is consistency in time reference
between measurements - if you are going to compare phase traces for timing info, the measurements
need to have been made with the same time reference. This is part and parcel of standard measurement
practice.
So the final question here is, is Smaart's phase trace accurate? Well, to answer this, I took my cue from
Mr. Danley and did a simple mag & phase response measurement of a HPF / LPF pair (12 dB/Oct
Butterworths at 80 Hz and 8 kHz respectively). Attached are three sets of measurement traces. The first
is data from a paper/post by Tom Danley (I am sorry, but I do not know the origin of the paper, as it
was forwarded to me) - which is what I based my filter setting on. I believe that this data was modeled,
not measured, but either way, it gives us a great view of what we should be seeing in our
measurements. It is our control for this experiment. (It is interesting to note however that because this
data was created through modeling, there is no inherent group delay in the system under test, no
ADC/DAC latency or propagation delays to contend with: T-zero is T-zero.) The second traces in Mr.
Danley's data shows the phase traces for two different measurement T-zeros, the first set to true T-zero
as before, and the second with a slightly later T-zero that corresponds to the "in-band" energy.
The second set of traces were measurements I made with Smaart (FPPO TF) of a digital processor with
the HPF/LPF pair engaged. To get my T-zero, I first did a measurement of the same processor without
the filters engaged and set my measurement T-zero with a simple delay measurement (purple trace). As
you can see, it is basically flat in mag and phase. Next, I engaged the HPF/LPF filter pair which
produced the Blue response trace (NOTE: the Green, White and Blue traces all match in magnitude 2020k, and in phase <500 Hz, so the White and Green traces are only visible where they deviate from
Blue trace). Next I increased the measurement by 0.02ms (1 sample) and obtained the green trace. Note
the change in the phase response trace above 500 Hz due to the change in time-reference for the
measurement. Next I used Smaart's AutoSm function (auto delay-locate) to set my measurement Tzero. As expected, it chose the HF of the in-band energy for its T-zero choice, since that energy creates
the highest peak in the impulse response - which is what AutoSm is locating. This changed my
measurement delay by another 0.02 ms and produced the White trace - which corresponds well with
Tom's Time = zero "in-band" trace above.
My Smaart Data
In examining the differences between the data I had pulled from Tom's paper/post from the data I
obtained through my Smaart measurements, I realized that the filters in the Danley paper did not
correspond to 2nd order Butterworths at 80 Hz and 8 kHz (looks more like 100 Hz and 5 kHz). So, to
check my work, and since I had already torn down my measurement set-up to reclaim desk space, I did
the easiest/laziest thing and asked Dave Gunness to model the Butterworths at 80 and 8k with his
FChart program. He then created the third set of traces below with the same three T-zero references.
Dave's FChart Data