On 2/8/13 2:15 AM, Ross Bencina wrote:
There are a at least two linear SVFs floating round now (the Hal
Chamberlin one and Andy Simper's [1] )
[1] http://www.cytomic.com/files/dsp/SvfLinearTrapOptimised.pdf
i've analyzed Hal's SVF to death, and i was exposted to Andy's design
some time ago, but at first glance, it looks like the "Trapazoidal SVF"
looks like it doubles the order of the filter. it it was a second-order
analog, it becomes a 4th-order digital. but his final equations do not
show that. do those "trapazoidal" integrators, become a single-delay
element block (if one were to simplify)? even though they ostensibly
have two delays?
i just did a quick check on the "Trapazoidal SVF", and it is identical
to using Bilinear Transform without pre-warping and applying BLT
directly to the analog filter. so it does not increase the order as it
first appeared to me to do.
it literally substitutes (assuming T=1):
s^-1 <--- (1/2)(1 + z^-1)/(1 - z^-1)
so they all become 2nd-order biquads and they can be represented in the
Direct Form (1 or 2) and compared directly to any other biquad design.
for the "bell" filter, assuming he gets the resonant frequency right
(which means dealing with the frequency warping effect), the only
possible net difference between *any* design is in how bandwidth or Q
turns out. all 2nd-order bell filters are equivalent in their
simplified transfer function except in how Q is defined. (well, i guess
that's not true for the Orfanidis design. that changes what the gain at
Nyquist is and doesn't make any difference if the resonance is more than
a couple octaves below Nyquist.)
now, what about Andy's "Optimised structure with all coefficients
remaining bounded [0, 2]"?
what is the basis for this structure? i can't seem to decode that, and
it also appears that the filter has 3 independent delay elements so it's
a 3rd-order digital filter emulating a 2nd-order analog filter. i just
would like to know where he came up with the structure of this.
we know that a digital filter can (if one allows for a little delay)
approach the behavior of an analog filter to as close fit as one desires
(as long as one is willing to increase the order of the filter and is
willing to accept the resulting delay). but i am curious to what the
basic philosophy of this Optimised structure is. while Andy explained
it for the Trapazoidal SVF, i can't tell by just looking at the drawing
for the Optimized what
--
r b-j r...@audioimagination.com
"Imagination is more important than knowledge."
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