Anatomy of a reverb algorithm

robert bristow-johnson <rbj@audioimagination.com> writes:
> [...]
> a good reverb is not all that inexpensive to implement. 

That's what I've been thinking. Needs a lot of memory and a lot of
processing power for long convolutions, even using frequency-domain
filtering.

> and then to keep the room modes at bay, you might need to slowly move
> the taps on a couple of the delays.

Are you talking about the room modes of the modeled room (the one the
impulse response being convolved describes)?
-- 
Randy Yates, DSP/Embedded Firmware Developer
Digital Signal Labs
http://www.digitalsignallabs.com

Max wrote:
> On Wed, 14 Sep 2016 14:41:58 -0500, Les Cargill
> <lcargill99@comcast.com> wrote:
>
>> Max wrote:
>>> I know that reverbs are normally built with all-pass and/or comb
>>> filters in various combinations.  Are there topologies that are more
>>> CPU-efficient, or more realistic?  I'm interested in small room
>>> emulation, but I need to keep up in real-time, and processing power
>>> may be limited.
>>>
>>> Obviously many common algorithms are just refinements of the the old
>>> Schroder algorithm, but that's a primitive and metallic sound. There
>>> must be  efficient modern algorithms that solve those problems. Any
>>> recommendations?
>>>
>>
>>
>> Effectively, all reverbs are convolutions of some sort.
>
> Purely convolutional reverbs are fairly CPU intensive. That's why I
> was looking at 'modeling' algorithms, which use allpass and/or comb
> filters.
>

Sure. That's why I gave a sort of estimate on how much power a convo. 
would use on one sort of processor.

Effectively, allpass/comb are doing a "simulation of a simulation". So
one might be able to use then as a test bench for an approach - if you 
can  take the impulse response of an approach, you can run it through
a convolver to test it.

>> A "metallic" reverb can be addressed by experimenting with filtering of
>> the response vector. But it really comes down to "more is better", at
>> least to a point. Pure comb filters have that "garden hose" flavor.
>
> I have a feeling that comb filters don't get as much love as they once
> did with the Schrodinger algorithm.
>

There's sort  of a reason for that :) There's a lot of the world now
that depends on 3.03 GHz processors for reverbs because they are
there, so that's where the action is.

>> I have and use the Waves IR convolution reverb, and this old machine (
>> 2012 vintage i5 dual-core 3.02 GHz) keeps up just fine. It'll consume,
>> say, 2-5% of this thing.
>
> That's pretty good.  I wonder if they doing some tricks to minimize
> the time-consuming convolutional steps.
>

Beats me. Convolution through FFT can be relatively cost effective. The
hard part is the delay and amortizing CPU use.

>> This stopped me from implementing one as a VST myself. I was able to get
>> a severely discounted price on the Waves Gold Bundle. Plan C was a
>> physical rackmount reverb device with S/PDIF I/O. I may do that anyway.
>> Let's just say that the build-vs-buy proposition has changed over the
>> years.
>
> I still love my Lexicons.
>

Yep. I wonder how far you'd get sampling the impulse response for those, 
then shoving that into a comb filter or whatnot. Obviously
handwaving at this point.

>> FAIR USE STYLE IP WARNING HERE!
>>
>> Realtime actual convolution is probably using some sort of proprietary
>> arrangement to keep the delay down.
>>
>> Here's the William G. Gardner paper. I dunno if you can just swipe the
>> algo. from it or not, but it should give you an idea:
>>
>> http://alumni.media.mit.edu/~adamb/docs/ConvolutionPaper.pdf
>>
>> And there's a demo that's ... pretty poorly executed ( but
>> understandably so ) , but it's an interesting project:
>>
>> https://www.youtube.com/watch?v=0Ebnue1a4vc
>
> Thanks, that was pretty cool. At least reassuring to see reverb
> running on a Beaglebone.
>

It's also a good starting point for audio on that sort of platform in
general. Not a well-adapted platform but the small form factor....

-- 
Les Cargill

On Friday, September 16, 2016 at 9:33:13 AM UTC-4, Randy Yates wrote:
> robert bristow-johnson <rbj@audioimagination.com> writes:
> > [...]
> > a good reverb is not all that inexpensive to implement.=20
>=20
> That's what I've been thinking. Needs a lot of memory and a lot of
> processing power for long convolutions, even using frequency-domain
> filtering.
>=20

i didn't mean those convolutional reverbs.  of course they are expensive an=
d fast-convolution (using FFT) is the only way to do them real time.  other=
wise you have something like a quarter million FIR taps.

> > and then to keep the room modes at bay, you might need to slowly move
> > the taps on a couple of the delays.
>=20
> Are you talking about the room modes of the modeled room (the one the
> impulse response being convolved describes)?

there are other reverb algs that they used with DSP hardware that does not =
model a **specific** room.  but is an LTI that models in generalities what =
happens in what we might call a nondescript "good" room.  like
1. direct path
2. early reflections (simple multitap delay line)
3. a pre-delay before the reverberant reflections
4. a diffuse and roughly exponentially decaying diffuse reverberant reflect=
ions.

that's sorta what the Schroeder comb and APF design and the Jot multiple fe=
edback design do.  it sounds like a room, but not any specific room.

and still, because the model has many fewer parameters than does a general =
convolutional reverb, the danger of resonating room modes is greater and on=
e way to deal with that is to slowly move the taps of a couple of delays in=
 feedback.  usually make one get longer while the other gets shorter so tha=
t there is no pitch bias.  this, of course makes the system time-variant, b=
ut you can't really tell so.

if you want Randy, i can send you a C file of a Jot 'verb i did back in the=
 previous decade to give you an idea.  (and since it doesn't slide the taps=
 around, the alg is LTI.) lemme know.

r b-j

>=20
> there are other reverb algs that they used with DSP hardware that does no=
t model a **specific** room.  but is an LTI that models in generalities wha=
t happens in what we might call a nondescript "good" room.  like
> 1. direct path
> 2. early reflections (simple multitap delay line)
> 3. a pre-delay before the reverberant reflections
> 4. a diffuse and roughly exponentially decaying diffuse reverberant refle=
ctions.
>
To all

I read this newsgroup because it often presents a learning opportunity for =
me and here is such a case.

re DSP reverbs.

and analogous to RF multi-path...

I understand how a DSP tapped delay line can provide discrete reflections o=
f whatever amplitude and delay and number desired.

I don't understand how diffuse delays are created in DSP.  In a room, I can=
 visualize a  sound impulse being reflected off a slanted surface in a way =
that the reflected impulse is diffuse.  How is this done in DSP?  Is it sim=
ply many many discrete taps close together that approximate a diffuse delay=
 or is it something else?

thanks

Mark

On Friday, September 16, 2016 at 2:41:43 PM UTC-4, mako...@yahoo.com wrote:
> >=20
> > there are other reverb algs that they used with DSP hardware that does =
not model a **specific** room.  but is an LTI that models in generalities w=
hat happens in what we might call a nondescript "good" room.  like
> > 1. direct path
> > 2. early reflections (simple multitap delay line)
> > 3. a pre-delay before the reverberant reflections
> > 4. a diffuse and roughly exponentially decaying diffuse reverberant ref=
lections.
> >
>=20
> I read this newsgroup because it often presents a learning opportunity fo=
r me and here is such a case.
>=20
> re DSP reverbs.
>=20
> and analogous to RF multi-path...
>=20
> I understand how a DSP tapped delay line can provide discrete reflections=
 of whatever amplitude and delay and number desired.
>=20
> I don't understand how diffuse delays are created in DSP.  In a room, I c=
an visualize a  sound impulse being reflected off a slanted surface in a wa=
y that the reflected impulse is diffuse.  How is this done in DSP?  Is it s=
imply many many discrete taps close together that approximate a diffuse del=
ay or is it something else?
>=20

please take a look at this paper.

 http://freeverb3vst.osdn.jp/doc/matlab_reverb.pdf=20

Google Schroeder reverb, Jot reverb, Gardner reverb, Griesinger reverb.
=20
the way that diffusion of the impulse response happens is with all-pass fil=
ters having disparate delays inside (some people think that the delays shou=
ld be related with mutual prime integer samples) being cascaded.  or even w=
ith one all-pass filter being contained inside another (an APF+delay replac=
ing the delay inside another APF).  so one impulse becomes several happenin=
g at weird time delays.  those feedback and cause *more* impulses at even w=
eirder time delays.  something like that.

r b-j

On Friday, September 16, 2016 at 2:41:43 PM UTC-4, mako...@yahoo.com wrote:

> I don't understand how diffuse delays are created in DSP.  In a room,
> I can visualize a  sound impulse being reflected off a slanted surface
> in a way that the reflected impulse is diffuse.  How is this done in
> DSP?  Is it simply many many discrete taps close together that
> approximate a diffuse delay or is it something else?

Given a sampled-time source, one can convolve the source with
any (known) continuous-time impulse response, and sample the result, 
without either incurring approximations or requiring infinite computation.

(If this is not obvious I can expand on why this his true.)

So there is no theoretical problem with creating an LTI digital reverb 
that is "diffuse" in the sense you describe.

RB-J's wandering tap delays may be more practical -- I am not sure,
I have never used that approach.

On the practicality/cost question, my premise is if you could sell
a digital reverb for under $10,000 in 1980 (the last time I worked
on them commercially), it does not require a lot of resources in
modern terms.

Steve

On Fri, 16 Sep 2016 11:09:13 -0700 (PDT), robert bristow-johnson
<rbj@audioimagination.com> wrote:

>On Friday, September 16, 2016 at 9:33:13 AM UTC-4, Randy Yates wrote:
>> robert bristow-johnson <rbj@audioimagination.com> writes:
>> > [...]
>> > a good reverb is not all that inexpensive to implement. 
>> 
>> That's what I've been thinking. Needs a lot of memory and a lot of
>> processing power for long convolutions, even using frequency-domain
>> filtering.
>> 
>
>i didn't mean those convolutional reverbs.  of course they are expensive and fast-convolution (using FFT) is the only way to do them real time.  otherwise you have something like a quarter million FIR taps.


I think part of the disparity in this thread has to do with
convolutional vs modeling (perceptual) approaches. I was discounting
convolutional approaches simply due to CPU load, but that's a good
point about memory as well.

It would also be nice to have continuously variable control over
parameters with minimal audio glitching, which is probably not in the
domain of convos.

>
>> > and then to keep the room modes at bay, you might need to slowly move
>> > the taps on a couple of the delays.

A lot of the CPU-economical algorithms that I've seen call for slow
variations in delays, etc to avoid perception of repeating patterns or
resonances.  I haven't experimented with that aspect, so I don't know
if the LFO patterns themselves could be perceived.  It seems like it
could lend an unrealistic sound though.

The techniques that I've been curious about are:
FDN: Feedback Delay Networks
DWN: Digital Waveguide Networks
Waveguide Mesh methods
SDN: Scattering Delay Networks

The latter was featured in a paper by Enzo De Sena and Julius O Smoth,
"Efficient Synthesis of Room Acoustic via Scattering Delay Networks":

https://arxiv.org/pdf/1502.05751.pdf

That references other papers by Vorlander, Savioja, and others, that
feature some of the other approaches above.

I was curious about whether anyone has experimented with those.

On Wed, 14 Sep 2016 09:54:21 -0400, Max <Max@sorrynope.com> wrote:

>I know that reverbs are normally built with all-pass and/or comb
>filters in various combinations.  Are there topologies that are more
>CPU-efficient, or more realistic?  I'm interested in small room
>emulation, but I need to keep up in real-time, and processing power
>may be limited.
>
>Obviously many common algorithms are just refinements of the the old
>Schroder algorithm, but that's a primitive and metallic sound. There
>must be  efficient modern algorithms that solve those problems. Any
>recommendations?

PS: A ref to another JOS paper on Digital Waveguide methods:
http://www.ece.uvic.ca/~bctill/papers/numacoust/Smith_Rocchesso_1997.pdf

I'm currently trying to parse various papers on DWN's, DWM's,
Scattering Delay Networks.  It seems that they're all advances on the
tradiitional modeling approaches with all-pass and comb filters.

SDN's in particular are intriguing because they're supposedly
CPU-economical, and their objective is accurate modeling of initial
reflections, with increasing approximation for less critical higher
order reflections. The end result should be way more accurate for room
modeling without the CPU expense of convolution.

But even the terminology is not mainstream (at least from what I can
discern).  Math symbology is different from the norm for DSP
references.  They must be building on math models outlined in
pioneering papers that I haven't seen yet.  So they're not an easy
read by any means.

Has anyone here experimented with this stuff?  Robert?

On Fri, 16 Sep 2016 11:41:39 -0700 (PDT), makolber@yahoo.com wrote:

>I don't understand how diffuse delays are created in DSP.  In a room, I can visualize a  sound impulse being reflected off a slanted surface in a way that the reflected impulse is diffuse.  How is this done in DSP?  Is it simply many many discrete taps close together that approximate a diffuse delay or is it something else?
>
>thanks
>
>Mark

Hi Mark,

Robert has already explained this, but in terms of convolutional
reverbs-- Often a blank pistol, a spark, or some other real-life
substitute for an impulse is used to collect the characteristic
response of a room, cathedral, or whatever.  Presuming LTI response,
that can be used to reproduce the acoustic characteristics of the
tested space.  

However, that's pretty CPU-expensive, so I was inquiring about
perceptual/modeling approaches, which Robert has described.

As well as the papers that you'll find via Google, there's a book by
Will Pirkle, "Designing Adio Effect Plug-ins in C++" that has info on
reverbs, and even includes a working environment that can both play
back samples thru the code, or create VST plugins for use with music
composition programs like Cubase.
 

Max  <Max@sorrynope.com> wrote:

>On Fri, 16 Sep 2016 11:41:39 -0700 (PDT), makolber@yahoo.com wrote:

>>I don't understand how diffuse delays are created in DSP.  In a room, I
>>can visualize a  sound impulse being reflected off a slanted surface in
>>a way that the reflected impulse is diffuse.  How is this done in DSP? 
>>Is it simply many many discrete taps close together that approximate a
>>diffuse delay or is it something else?
>>

>Hi Mark,

>Robert has already explained this, but in terms of convolutional
>reverbs-- Often a blank pistol, a spark, or some other real-life
>substitute for an impulse is used to collect the characteristic
>response of a room, cathedral, or whatever.  Presuming LTI response,
>that can be used to reproduce the acoustic characteristics of the
>tested space.  

I see a distinction between diffuse reflections, and echo
density.  Echo density is an overall metric in units of reflections
per second and might be uniform along the time axis,, whereas diffuse 
reflections are individually spread along the time axis but are still distinct reflections.

In either case, the characteristic can be simulted/implemented in
discrete time.

Steve