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Re: Interpolation schemes and SB Live!

Date1998-10-22 15:40
FromHans Mikelson
SubjectRe: Interpolation schemes and SB Live!
Hi,

>The problem is that the first order filters that are implemented in the
waveguide opcodes
>don't use fractional delay, so the pitch of high notes is not precise.

There is a paper on fractional waveguide filters at:


http://www.hut.fi/Yksikot/Akustiikka/publications/vesa_phd.html

Bye,
Hans Mikelson



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From: Josep M Comajuncosas 
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To: Gabriel Maldonado 
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Subject: Re (II): Interpolation schemes and SB Live!
References: <362E5DB3.43AB74F6@intercom.es> <362F1E6D.746B372E@agora.stm.it>
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Gabriel Maldonado wrote:

> Where is it possble to get the algorithm to implement 8 point interpola=
tion? If I could
> see an example of it I will implement it in Csound.

Hi,
as I see you=B4re interested in the subject,
here it is the general formula for a Nth order Lagrange interpolator,
it works as a FIR structure and has an inherent lowpass behaviour,
but implements very accurately the fractional delay,
further references in T.Tolonen & Vesa V=E4lim=E4ky works.

Josep M Comajuncosas


This is a PS to text translation of their Thesis:

h(n) =3D mult (from k=3D0, k=3D!n to N) [(D-k)/(n-k)] for n=3D 0,1,2,...N=
 (3.63)
where D is the fractional delay and N the order of the FIR filter.

Computation of Coefficients for a Lagrange Interpolator

The first=ADorder Lagrange interpolator corresponds to the well=ADknown
linear interpola=AD
tion. The coefficients are obtained from Eq. (3.63) with N =3D 1 as
h(0) =3D 1- D , h(1) =3D D
(3.72)
Note that in the first=ADorder case D =3D d since the integer part of D i=
s
zero.

The formulas for the filter coefficients of the Lagrange interpolator
with N =3D 2 are
h(0) =3D (1/2)(D -1)(D - 2)
h(1) =3D -D(D - 2)
h(2) =3D (1/2)D(D -1)
(3.73)

and with N =3D 3,
h(0) =3D -(1/6)(D -1)(D - 2)(D - 3)
h(1) =3D (1/2)D(D - 2)(D - 3)
h(2) =3D -(1/2)D(D -1)(D - 3)
h(3) =3D (1/6)D(D -1)(D - 2)
(3.74)

In general, the coefficients h(n) of the Lagrange interpolator are
determined by an
Nth=ADorder polynomial in D. This implies that N additions and N
multiplications per
coefficient are required to evaluate its value for a given D.
Altogether, it takes
N(N +1) =3D N 2 + N additions and N 2 + N multiplications to update all
the N coeffi=AD
cients. An efficient procedure to update the coefficients of a Lagrange
interpolator was
introduced in V=E4lim=E4ki (1992, Appendix A):

1) evaluate the differences D -- 1, D -- 2, ..., D -- N;
2) evaluate the products D(D -- 1), (D -- 2)(D -- 3), ..., (D -- N +
1)(D -- N);
3) evaluate the coefficients h(0), h(1), ..., h(N) by multiplying the
results of Steps 1
and 2 and constant coefficients.

Using this technique, the computational burden of evaluating the
coefficients of an Nth=AD
order interpolator consists of N additions (subtractions) and less than
N 2 + N multipli=AD
cations.
For example, computing the values of the four coefficients of a
third=ADorder Lagrange
interpolator using this method requires 3 additions and 10
multiplications. This is a
remarkable saving when compared to 12 additions and 12 multiplications
that would be
required were the straightforward polynomial evaluation used.
The most efficient practical solution to the updating of interpolating
coefficients is to
use table lookup. In software implementations this is usually the
fastest way, and thus
most recommendable, provided that the required memory space is
available.

> > Another question related to waveguide opcodes. Does deltapi (and dela=
yw
> > btw) accept fractional sample delay lengths (well, fractional 1/kr
> > units) ?
>
> Yes it does.
>
> The problem is that the first order filters that are implemented in the=
 waveguide opcodes
> don't use fractional delay, so the pitch of high notes is not precise.

Hmm a serious handicap.



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From: Hans Mikelson 
To: Csound 
Subject: Create Halloween Sound Effects with Spatializer Orc/Sco
Date: Thu, 22 Oct 1998 10:43:02 -0500
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Hidyho Csounders,

If you are like me then you have been busy decorating the outside of your
house with cob-webs, skeletons, dummies, transforming the front yard into a
graveyard, installing motion sensor triggered special effects, smoke
machines, black lights and strobe lights.  No Halloween house would be
complete without some spooky sound effects.

First go pick some spooky sounds from your local internet haunted sound
depot:

http://www.geocities.com/Heartland/Meadows/6158/story/hhsound.html

This is a good start but mono sounds are not going to cut it for Halloween.
You want owls hooting in the tree above your head, wolves howling all around
you, cackling witches whizzing past on broomsticks, organs playing in a
cathedral and beasts trying to bite your head off.

Now you can animate those dull lifeless Halloween sounds with my handy-dandy
spatial audio generator to make truly bone-chilling, spine-tingling effects.
Merely insert your soundin.? file into the spatializer, specify x, y
coordinate paths and let your sounds come alive:

; ORCHESTRA
;---------------------------------------------------------------------------
-------
; Spatial Audio
; Coded by Hans Mikelson October 1998
; This spatial audio system included the following features:
;
;  1. Moving sound source with table supplied moving X and Y coordinates
;  2. Volume decreases as 1/r^2
;  3. Filtering of sound due to air absorption
;  4. Doppler effect due to moving sound
;  5. Simplified HRTF for head shadow filtering
;  6. Inter ear time delay
;  7. Speaker cross-talk cancellation based on both inter ear time delay &
head shadowing
;---------------------------------------------------------------------------
-------
sr=44100
kr=22050
ksmps=2
nchnls=2
zakinit 30,30
;---------------------------------------------------------------------------
-------
; Disk Input Mono
;---------------------------------------------------------------------------
-------
        instr  4
iamp    =      p4
irate   =      p5
isndin  =      p6
ioutch1 =      p7
ain1    diskin isndin, irate
        zawm   ain1, ioutch1
        endin
;---------------------------------------------------------------------------
-------
; Disk Input Stereo
;---------------------------------------------------------------------------
-------
        instr  5
iamp    =      p4
irate   =      p5
isndin  =      p6
ioutch1 =      p7
ioutch2 =      p8
ain1, ain2 diskin isndin, irate
        zawm   ain1, ioutch1
        zawm   ain2, ioutch2
        outs   ain1*iamp, ain2*iamp
        endin

;---------------------------------------------------------------------------
-------
; Spatial Audio
; Coded by Hans Mikelson October 1998
;---------------------------------------------------------------------------
-------
        instr     11
idur    =         p3            ; Duration
iamp    =         p4            ; Amplitude
iexl    =         p5            ; Fixed left ear location X coordinate
iexr    =         iexl+.23      ; Fixed right ear location X coordinate
iey     =         p6            ; Fixed ear location Y coordinate (facing +Y
axis)
isxtab  =         p7            ; Moving source table for X coordinate in m
isytab  =         p8            ; Moving source table for Y coordinate in m
iinch   =         p9            ; Audio input channel
ihrtabl =         p10           ; Head shadowing filter for left ear
ihrtabr =         p11           ; Head shadowing filter for right ear
imax    =         500           ; Maximum delay time in ms
ipi     =         3.14159265    ; Pi
ics     =         .333          ; Approx. speed of sound in m/ms
kamp    linseg    0, .002, iamp, idur-.004, iamp, .002, 0 ; Declick
Enevelope
ksx     oscil     1, 1/idur, isxtab                       ; Moving Source X
ksy     oscil     1, 1/idur, isytab                       ; Moving Source Y
ksmexl  =         ksx-iexl                                ; Delta X left
ksmexr  =         ksx-iexr                                ; Delta X right
ksmey   =         ksy-iey                                 ; Delta Y
kdistl  =         sqrt(ksmexl*ksmexl+ksmey*ksmey)         ; Distance from
left ear to source
kdistr  =         sqrt(ksmexr*ksmexr+ksmey*ksmey)         ; Distance from
right ear to source
kdistlnz=         (kdistl==0 ? 1 : kdistl)                ; Avoid divide by
zero problem
kdistrnz=         (kdistr==0 ? 1 : kdistr)                ; Avoid divide by
zero problem
kangl   =         cosinv(ksmexl/kdistlnz)                   ; Get the
magnitude of the angle (0 to Pi)
kangr   =         cosinv(ksmexr/kdistrnz)                   ; Get the
magnitude of the angle (0 to Pi)
ksmeynz =         (ksmey==0 ? 1 : ksmey)                  ; Make sure it is
not zero
ksign   =         ksmeynz/abs(ksmeynz)/2/ipi              ; Get the sign
kanglel =         kangl*ksign                             ; Get the true
angle -Pi to Pi
kangler =         kangr*ksign                             ; Get the true
angle -Pi to Pi
kdd4l   =         kdistl/4                                ; Factor for
distance and air absorption
kdd4r   =         kdistr/4                                ; Factor for
distance and air absorption
ain     zar       iinch                                   ; Input audio
adoppl  vdelay    ain/(1+kdd4l*kdd4l), kdistl/ics, imax   ; Volume decreases
as distance^2.
adoppr  vdelay    ain/(1+kdd4r*kdd4r), kdistr/ics, imax   ; Volume decreases
as distance^2.
                                                          ; arrival time is
delayed by speed of sound, doppler effect
afltail butterlp  adoppl, 20000/(1+kdd4l)                 ; Air absorption
of distant sound
afltair butterlp  adoppr, 20000/(1+kdd4r)                 ; Air absorption
of distant sound
khrtfl  tablei    kanglel, ihrtabl, 1, .5                 ; Get the "poor
man's" HRTF for left ear
khrtfr  tablei    kangler, ihrtabr, 1, .5                 ; Get the "poor
man's" HRTF for right ear
ahrtfl  butterlp  afltail, khrtfl                         ; Apply the filter
for head shadowing left ear
ahrtfr  butterlp  afltair, khrtfr                         ; Apply the filter
for head shadowing right ear
asctcl  butterlp  ahrtfl, 8000                            ; Simplified head
shadowing for speaker cross-talk
asctcr  butterlp  ahrtfr, 8000                            ; Simplified head
shadowing for speaker cross-talk
asctcdl delay     asctcl, .0003                           ; Speaker
cross-talk cancellation delay left
asctcdr delay     asctcr, .0003                           ; Speaker
cross-talk cancellation delay right
        outs      (ahrtfl-asctcdr)*kamp, (ahrtfr-asctcdl)*kamp ; Cancel
speaker cross-talk and ouput

        zacl      iinch, iinch                            ; Clean up the zak
channel
        endin

; SCORE
;   Sta  Dur   Amp  Pitch  SoundIn  OutCh
i4  0.0  2.61  0.0  1      1        1
i4  3.0  1.52  0.0  1      3        2
i4  4.0  4.38  0.0  1      2        1
i4  8.0  1.86  0.0  1      4        1
i4  6.0  5.44  0.0  1      5        2

f4 0 1024 -7  16000 128 12000 384  3000 128  8000 256 20000 256 16000 ; HRTF
Left
f5 0 1024 -7   8000 128  3000 384 12000 128 16000 256 20000 256  8000 ; HRTF
Right
f10 0 1024 -7    12  512  25  512 15                   ; Moving Source X
f11 0 1024 -7    7   256  7   256  8  256   9 256  15  ; Moving Source Y
f12 0 1024 -7    18  512  23  512 15                   ; Moving Source X
f13 0 1024 -7    18  256   9  256  8  256   9 256  15  ; Moving Source Y
; 2D Echos
;    Sta  Dur  Amp  EarX  EarY  SourceX  SourceY  InCh  HRTFL  HRTFR
i11  0.0  10.0 .5   20    10    10       11       1     4      5
i11  3.0  10.0 .5   20    10    10       12       2     4      5




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From: Dave Perry 
To: csound@maths.ex.ac.uk
Date: Thu, 22 Oct 1998 20:51:26 -0700
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Subject: ANNOUNCE : Visual Orchestra no longer available from Demon
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This is to announce that the new download site for Visual 
Orchestra,  the Windows Csound GUI is:



The old download site  will be 
offline in the next few days.

thanks,

Dave Perry
email : perry@student-kmt.hku.nl




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Date: 22 Oct 98 14:51:41 EDT
From: "Matt J. Ingalls" 
Subject: Csound 3.49.1 PPC
To: "Sarah E. Meyers" , 
    "Peter M. Traub" , 
    "Owen R. Grace" , 
    "Michael C. Frengel" , 
    "Douglas I. Repetto" , 
    "Lily Anne N. Perez" , 
    Taehong Park , 
    "Charles M. Dodge" , 
    "Douglas I. Repetto" , 
    Larry Polansky , 
    Kui Dong , csound@maths.ex.ac.uk
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hi everyone,

	i just put a new version of mac PPC csound on the ftp:

ftp://mills.edu/ccm/csound.ppc/Csound3.49.1PPC.sit.hqx

a bit of the README below...

because of upgrade to CWP4, some things have changed most
notably the MIDI code - which hasnt been tested - so if you
could report any bugs that would be a great help.
-matt
=======================================
oct22.98
	Csound for Power Macintosh
=======================================
This Version: 
	fFitch code base	3.49
	Perf "engine"		3.49.1
	Csound "front end"  1.1.1
	
Available From:
	ftp://mills.edu/ccm/csound.ppc
=======================================
changes from 3.485 (front end 1.0.0)
=======================================
Perf:
- Upgraded source to 3.49 
- ReEnabled User-Settable screen buffer 
- Fixed Saved Command Line bug losing last char
- Fixed AIFF-C bug not compatible with Soundhack
	(thanks to tom erbe for help)
- Internal MIDI changes with merge may have 
	improved MIDI or made implementation worse(?)
	
Front End:
- Fixed bug in score generator autogen
- Added option to not display output window
	when saving as a listing file
- Reflected newly added ability to use a 
	"Goggins-Style" one file (*.csd) instead
	of orc/sco combination
- Due to compiler upgrade, now an optimiztion conflict in
	score generator - as a result front end is not 
	entirely optimized - noticeable effect is unknown.
=======================================
Please email bugs to csound-dev@mills.edu


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Date:     Thu, 22 Oct 98 20:56:21 BST
From: jpff@maths.bath.ac.uk
Subject:  Csound versi0on 3.49
To: csound@maths.ex.ac.uk
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Message written at 21 Oct 1998 10:01:43 +0100

I placed the sources, binaries and release notes on
	 ftp://ftp.maths.bath.ac.uk/pub/dream/newest/ 
late on Tuesday as I knew that I would be out of contact for a few
days (*) and as the system seems reasonably robust, and there are real
bugs in at least the SGI version for 3.48x, I thought I would slip
them out and see who notices.  The release notes are more or less as
in the draft, except I completed some opcode descriptions.  The system
also has a scheme for accepting a single unified file of orchestra and
score, but that is still rather incomplete -- it works but the code
for setting options and such is not written yet.  The design follows
that of Michaeel Gogins, which he uses for AXCsound.  I suggest that
you use this facility with care.  For 3.50 (yes there will be one) I
intend completing this as well as some other things currently in draft
here. 
  I will place the SGI binary on the server as soon as I can (Friday?)
and also the SUN one.  I expect MAC and Linux systems to be ready by
then also.

I hope you all enjoy this release, and make good music with it

==John ffitch


* looking for a job;  anyone have a vacancy for an aging expensive
  academic/hacker? 


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Subject:  SGI operating system query
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Message written at 22 Oct 1998 15:42:18 +0100

The computer support staff in Bath have proposed that all out SGIs be
upgraded to Irix6.3 in order to solve the Y2K problem.  This would
mean that I would be unable to generate an Irix5.3 binary (although a
4.0.5F is likely to continue!).  My question is would the lack of a
5.3 system inconveninece anyone?  I may still me able to influence
changes here, but it is not worth doing it unless there is a real
need.  It may be that everyone with SGI also has compilers in which
case I do not have to be too concerned with providing binaries
anyway.  Or it could be a real pain for someone.  Let me know please.
==John ffitch


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From: Scott Lipscomb 
To: 'CSound Discussion List' 
Subject: psychoacoustic demonstrations
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Greetings, folks!

I have been searching all of the various CSound-related sights hoping to
find an answer in the Discussion List FAQ or on the variety of
Orchestra/Score sites, but have come up empty handed ... that brings me
to you, collectively.

I teach a variety of classes here at UTSA, many of which address the
topic of psychoacoustics.  I am attempting to find a repository of sound
files (public domain) that provide aural demonstrations of some of the
more common auditory illusions (e.g., pitch circularity as demonstrated
in the Shepard Scale [Shepard, 1964], Risset's gliding tone that
illustrates the same concept, etc.) and other related psychoacoustic
phenomena.  Is there a collection of orchs & scores anywhere in
existence that would contain some of these materials? either in sound
file format or in orch/score combinations?

Thanks in advance for your response to a novice CSound user!

Sincerely,
Dr. Scott D. Lipscomb
Assistant Director, Assistant Professor, and Undergraduate Advisor of
Record
UTSA Division of Music
6900 N. Loop 1604 West
San Antonio, TX  78249
(210) 458-4354
(210) 458-4381 FAX
lipscomb@utsa.edu
http://music.utsa.edu/~lipscomb/



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From: Michael Gogins 
To: Gabriel Maldonado 
Cc: Csound list , 
    "Boulanger, Richard" 
Subject: Re: Interpolation schemes and SB Live!
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Gabriel, there was a presentation on this at the ICMC that you can find i=
n
your Proceedings:

Roger Dannenberg, "Interpolation Error in Waveform Table Lookup", page 24=
0.

You could email Dannenberg to see if he has suggestions on the best way t=
o
do this in Csound.

By the way, I had a chat with Jim Wright from IBM about using TCP/IP or U=
DP
as a protocol for MIDI. He was against it because delivery latency cannot=
 be
guaranteed with straight IP. He suggested that FireWire be used, and said=
 he
was looking into it.

Coincidentally, I ran into the following Web page when doing my semi-regu=
lar
Web search for Csound related stuff:

http://www.pavo.com/index.htm.

This is a very interesting site because this outfit appears to be working
with Analog Devices on an Extended Csound related project, and with Yamah=
a
on a FireWire protocol for both multi-channel real-time digital audio, an=
d
MIDI information.

I think we should talk to the Pavo people and see what the specification =
of
their FireWire protocol is, and whether any manufacturers (Yamaha?) are
going to make controllers for it. If so, it might be a good choice to put
into Csound.


-----Original Message-----
From: Gabriel Maldonado 
To: Josep M Comajuncosas 
Cc: csound@maths.ex.ac.uk 
Date: Thursday, October 22, 1998 8:17 AM
Subject: Re: Interpolation schemes and SB Live!


Josep M Comajuncosas wrote:
>
> Hi all,
> I recently saw the promotional prospectus of a low-cost PC sound card
> (called MaxiSound or so) and I was *really* disapointed with its specs.
> compared to Csound. Specifically, it is said to use a 3rd order
> polynomial scheme for wavetable interpolation, when Csound only accepts
> linear (1st order) interpolation.
> As you may agree this cannot be accepted ;-), I=B4d suggest at least 3 =
new
>
> opcodes, called maybe
> oscilp
> tablep
> deltapp
> with an additional parameter to choose the polynomial degree used for
> interpolated readout.
> I=B4m not very sure about the improvement in the s/n ratio and in the
> frequency response in relation to the degree of the Lagrange
> interpolator. Maybe some of you have any clues. But it would be nice to
> implement such feature.

The problem is: does it improve the sound quality? How much does it cost =
in
processing
speed?
My new SoundBlaster Live has an internal wavetable synthesizer who does 8
point
interpolation in realtime. Actually the sound quality is excellent. I don=
't
know if it
depends of the interpolation algorithm or of the hardware analog converte=
r.

Where is it possble to get the algorithm to implement 8 point interpolati=
on?
If I could
see an example of it I will implement it in Csound.



> Another question related to waveguide opcodes. Does deltapi (and delayw
> btw) accept fractional sample delay lengths (well, fractional 1/kr
> units) ?

Yes it does.


> If not, is it expected to implement it soon? Otherwise it could
> be difficult to tune a delay line at a precise high frequency, esp. at
> low k-rates.
> This is specially noticeable when developing waveguide models.

The problem is that the first order filters that are implemented in the
waveguide opcodes
don't use fractional delay, so the pitch of high notes is not precise.


--
Gabriel Maldonado

http://www.agora.stm.it/G.Maldonado/home2.htm



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From: Larry Troxler 
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    "Boulanger, Richard" 
Subject: Re: Interpolation schemes and SB Live!
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A couple of observations/questions:

-   When I was using Csound, I would simply use a large enough table
size, so that the error created by using only linear (or none at all)
interpolation, was less then the resolution of the output file type (in
my case, 16 bits). On today's machines, using 64K for a wavetable isn't
a big deal. I suppose the tradeoff is that there the RAM cache will be
overwhelmed on certain processors, hence making interpolation
preferable. 

-  At what point, does Sinc interpolation (which, is the theoretically
correct approach) become more cost effective (in terms of fidelity per
computation time) then polynomial interpolation? Without really
analyzing the tradeoffs, my initial response to a proposal to a proposal
to use say, eight-point poly interpolation, would be that surely a Sinc
interpolation with lesser points would give better results. But perhaps
not, especially given that the implementation of a Sinc interpolation
might need to involve a second table lookup to efficiently compute the
sinc function!

Well, in summary, (a) Why not just use larger table sizes where the
interpolation method isn't an issue, and (b) what are the tradeoff
points with polynomial vs. Sinc interpolations? 

Larry
    

--  Larry Troxler --  lt@westnet.com  --  Patterson, NY USA  --



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From: Mike Berry 
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To: Michael Gogins , 
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Subject: Re: Interpolation schemes and SB Live!
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	I have recently implemented UDP control of GrainWave using the Open
Sound Control (OSC) kit from CNMAT.  We are still getting a few bugs
out, but the system is able to provide quite solid performance, even
over a 33.6 modem line.  OSC has a timing system in it, so everything is
timetagged so that it can be played on schedule.  We are presently
simply encapsulating MIDI messages inside OSC packets, but the facility
is there to expand to other protocols.  OSC is platform independant -
all you need to do is add a UDP receiver and sender.  You can get info
and the SDK at:

 http://cnmat.CNMAT.Berkeley.EDU/OSC


-- 
Mike Berry
mikeb@nmol.com
http://www.nmol.com/users/mikeb




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Greetings
    Upon testing the new midi envelope I've found that it dosen't work.  I'm
assuming that there is a note off sensor for the release stage, but it
dosen't seem to trigger.  Also the Winsound interface dosen't seem to
remember if one sets the "T" flag or not.
Good Luck,
Ken



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Date: Thu, 22 Oct 1998 19:34:11 -0400
From: Charles Baker 
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To: Larry Troxler , csound 
Subject: Re: Interpolation schemes and SB Live!
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Larry Troxler wrote:

..some helpful, insightful stuff, then questions himself, saying

>perhaps not, especially given that the implementation of a Sinc
interpolation
>might need to involve a second table lookup to efficiently compute the
sinc function!

Well, absolutely, you need the second lookup...
but the second lookup still is much faster even though
you will still have to window the Sinc interpolation function, anyway...
 as  to polynomial interpolation.. as I understand it
(and you evidently also opine) the polynomial calculation expense grows
quite
high for orders that produce useful results, and if you can afford the
memory 'cost' of large table size & the sinc  & window tables for
filtering,
you can easily beat polynomial interpolation. In fact , I don't even think
the
sinc 'filter' has to be that many points, although again to get enough
'resolution'
in the appropriatly sampled sinc func, you should use a large enough sinc
function
or use some sort or (usually linear ;) ) interpolation in reading the sinc
function!
And still, I understand this algorithm clocks out faster than equivalently
clean
polynomial interpolation algorithms!!

charlieb



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From: Gabriel Maldonado 
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I think you are right about the fact that a big table can make multi-point interpolation
useless. Actually, in the case of a sine wave I find that even a 1024 point table, readed
by the oscili opcode, sounds very very good at any frequency. The problem rises when using
sound samples (for example with loscil). In this case the table is filled by a set of
samples already existent, and the user cannot modify them. Also in this case the computer
memory is not so big to expand the wavefile length and interpolate the samples by means of
good a wave editor.

BTW What is the difference beetween Sinc interpolation and polynomial interpolation
(excuse my math ignorance).

Gabriel



Larry Troxler wrote:
> 
> A couple of observations/questions:
> 
> -   When I was using Csound, I would simply use a large enough table
> size, so that the error created by using only linear (or none at all)
> interpolation, was less then the resolution of the output file type (in
> my case, 16 bits). On today's machines, using 64K for a wavetable isn't
> a big deal. I suppose the tradeoff is that there the RAM cache will be
> overwhelmed on certain processors, hence making interpolation
> preferable.
> 
> -  At what point, does Sinc interpolation (which, is the theoretically
> correct approach) become more cost effective (in terms of fidelity per
> computation time) then polynomial interpolation? Without really
> analyzing the tradeoffs, my initial response to a proposal to a proposal
> to use say, eight-point poly interpolation, would be that surely a Sinc
> interpolation with lesser points would give better results. But perhaps
> not, especially given that the implementation of a Sinc interpolation
> might need to involve a second table lookup to efficiently compute the
> sinc function!
> 
> Well, in summary, (a) Why not just use larger table sizes where the
> interpolation method isn't an issue, and (b) what are the tradeoff
> points with polynomial vs. Sinc interpolations?
> 
> Larry
> 
> --  Larry Troxler --  lt@westnet.com  --  Patterson, NY USA  --

-- 
Gabriel Maldonado

http://www.agora.stm.it/G.Maldonado/home2.htm



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From: jpff@maths.bath.ac.uk
Subject:  Re: Interpolation schemes
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Message written at 22 Oct 1998 22:25:37 +0100
--- Copy of mail to gelida@intercom.es ---

Improved intepolation was on my list after ICMC; have not got round to
it yet.
==John ffitch


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From: jpff@maths.bath.ac.uk
Subject:  Reverb question
To: csound@maths.ex.ac.uk
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Message written at 23 Oct 1998 11:32:21 +0100

This is a question expecting the answer no (as I remember from
learning latin). 

Does anyone have the impulse-response of the Cathedral of the
Dormition in Smolensk?

I ask as it seems to have a very sweet sound judging by a recording of
the USSR Ministry of Culture Chamber Choir I have, and I would like to
use it.

==John ff