Just realized that the following answer has never made its way through
to the list.
@Robert: I believe it has to do with your mail client settings, which
override the "reply-to" field. So it's quite possible that more answers
to your mails do not get to the list. Or is that on purpose?
Hi Robert
On 24-Jul-15 21:48, robert bristow-johnson wrote:
in the 2nd-order analog filters, i might suggest replacing "2R" with
1/Q in all of your equations, text, and figures because Q is a
notation and parameter much more commonly used and referred to in
either the EE or audio/music-dsp contexts.
I'm not such a big friend of the Q notation. My guess is that the Q
parameter was introduced originally for something like radio tuning
LC-circuits, where it makes perfect sense. For music 2-pole filters the
problem is that Q changes from +inf to -inf during the transition into
the selfoscillation region. OTOH, the R parameter is simply crossing the
zero. Also see the footnote on page 84 of the rev 1.1.1. The R parameter
also nicely maps to the pole position, being simply the cosine of the
polar angle, while the cutoff is the radius. So the pole's coordinates
are simply -w*cos R, +-w*sin R (for |R|<=1).
in section 3.2, i would replace n0-1 with n0 (which means replacing
n0 with n0+1 in the bottom limit of the summation). let t0
correspond directly with n0.
On one hand makes sense. OTOH, using zero-based array indexing, like in
C, n0 is intuitively understood as the first output sample. I agree,
this is less conventional mathematically, but from a software
developer's point of view this might be more intuitive. So, to an
extent, I believe this is a matter of taste and intention.
now even though it is ostensibly obvious on page 40, somewhere (and
maybe i just missed it) you should be explicit in identifying the
"trapezoidal integrator" with the "BLT integrator". you intimate
that such is the case, but i can't see where you say so directly.
p.40, directly under (3.5)
"The substitution (3.5) is referred to as the bilinear transform, or
shortly BLT.
For that reason we can also refer to trapezoidal integrators as BLT
integrators."
Not good enough?
section 3.9 is about pre-warping the cutoff frequency, which is of
course oft treated in textbooks regarding the BLT. it turns out
that any *single* frequency (for each degree of freedom or "knob")
can be prewarped, not only or specifically the cutoff.
Bottom of p.43
"Notice that it's possible to choose any other point for the prewarping,
not necessarily the cuto ff point....." etc
in 2nd-order system, you have two independent degrees of freedom that
can, in a BPF, be expressed as two frequencies (both left and right
bandedges). you might want to consider pre-warping both, or
alternatively, pre-warping the bandwidth defined by both bandedges.
That's a good point. This approach is used in 7.9 but you're right, it
should have been introduced in chapter 5.
lastly, i know this was a little bit of a sore point before (i can't
remember if it was you also that was involved with the little tiff i
had with Andrew Simper), but as depicted on Fig. 3-18, any purported
"zero-delay" feedback using this trapezoidal or BLT integrator does
get "resolved" (as you put it) into a form where there truly is no
zero-delay feedback. a "resolved" zero-delay feedback really isn't
a zero-delay feedback at all. the paths that actually feedback come
from the output end of a delay element. the structure in Fig 3-18
can be transposed into a simple 1st-order direct form that would be
clear *not* having zero-delay feedback (but there is some zero-delay
feedforward, which has never been a problem).
The structure in 3.18 clearly doesn't have ZDF (although I don't think
it can be made equivalent to any of direct forms without changing its
topology and hence the time-varying behavior). That's the whole point of
the illustration. However, once you get used to the ZDF, I'd say that
it's probably much easier and more intuitive to stick to ZDF structures
like 3.12 and understand the resolution implicitly (or actually even
directly 2.2, you can notice that afterwards the book hardly uses any
discrete-time diagrams). Particularly, when nonlinearities are
introduced into the structure, thereby leaving you the freedom of
choosing the numerical approach to treat them (post-resolution
application, Newton-Raphson, analytical solution, "mystran's method" etc).
i'll be looking this over more closely, but these are my first
impressions. i hope you don't mind the review (that was not
explicitly asked for).
Would be highly appreciated. And thanks for the comments which you
already made.
Regards,
Vadim
--
Vadim Zavalishin
Reaktor Application Architect | R&D
Native Instruments GmbH
+49-30-611035-0
www.native-instruments.com
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