Re: Fraction saving. Was "a question about IIR filter"

On Oct 8, 12:42 pm, Randy Yates <ya...@xxxxxxxx> wrote:
Jerry Avins <j...@xxxxxxxx> writes:
qittykat2001 wrote:

...

Thanks Jerry, could you pls explain the fraction saving a little bit?
Sorry I am really a newbie in DSP area.

Not a lot of people are familiar with it. When I thought I invented
it, I called it "remainder saving". It turns out that R.B-J. invented
it before me, and I use his name for the technique. A more descriptive
name is "truncated-part accumulation".

I was introduced to it back in 1997 at GEC Marconi Hazeltine (New
Jersey) when working with Don Heckathorn of Lincoln Labs. He called it
fraction saving.

in fact, it was from Randy that i first heard the term "fraction
saving" and i ran with it. before i called it "first-order noise
shaping with a zero at DC". that's not as compact as "fraction
saving" or "remainder saving". "truncated-part accumulation" is not
as compact, either.

and i most certainly did not invent it. i first saw it in an old Jon
Dattorro paper regarding digital filter structures in the Nov. 1988
AES Journal (which coincidently also had my first published paper in
it).

i might have become a big cheerleader for the technique, since the
time (sometime in the '90s) that i realized that this "fraction
saving" or "remainder saving" or "first-order noise shaping with a
zero at DC" or "truncated-part accumulation" or whatever you want to
call it can be used to inexpensively blow away a particular limit-
cycle problem that fixed-point IIR filters have that appears when you
switch (or fade) the input to dead silence (with actual zeros going
into the input) and the output gets stuck at some very low level DC.
and even though the DC is at a very low level, it's high enough that
it can show up as -60 dB on a digital VU meter (it's dead silence, but
your VU meter doesn't go to -inf dB as it should) and can quietly
click when you switch the filter out of the stream (expecting it to be
a wire and quiet) or splice audio that was so filtered to audio that
was not (even though the splice happens at a moment of "silence") or
to audio filtered with a different filter. that was so annoying and
this "fraction saving" was such a cheap and effective way to dispatch
that bug to oblivion, that i became a big believer in using the
technique regularly (at every truncated node) for fixed-point IIR,
even at times that generating and adding dither seems too expensive.

if there is a serious word-width reduction, like to 16-bits for
mastering to CD, then the expense of proper TPDF dithering, possibly
with some very high-order noise shaping is worth it. but i *still* do
not see what any of these fancy-smancy commercial dithering and word-
width reduction algs, like UV22 http://www.apogeedigital.com/products/uv22hr.php
have to offer over high-pass TPDF dither, or white TPDF dither with
psycho-acoustically shaped noise-shaping in the feedback. maybe i can
learn something here.

if i can claim any novelty, i might have been the first to realize
that fixed-point IIR DC blocking filters have the same limit-cycle
problem and that this "fraction saving" can cure it there also. it's
gotta be annoying if you put in a DC blocking filter to block DC and
the goddam DC blocking filter generates its *own* DC upon dead-silent
input.

r b-j


.

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