The integrtator is an IIR LP filter, so it will produce a signal with a certain amount of DC as it has a pole at 0Hz. The code assumes this to be about 0.5 and tries to remove it. I'd say a more robust approach is to use a DC blocker.

Victor 

----- Original Message -----
From: ebmtranceboy <ebmtranceboy@gmail.com>
Date: Wednesday, September 21, 2011 6:37 pm
Subject: [Csnd] unexpected integ offset
To: csound@lists.bath.ac.uk

> Hi all,
> Sorry in advance if this is not the right place to ask this kind of
> question.
> I'm trying to understand the following instrument and I'm 
> puzzled by the
> "asaw = asawdc - .5" line
> 
> ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
> instr 1; band limited sawtooth wave
> ; coded by Josep M Comajuncosas / jan98
> ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
> 
>    iamp    
> =      10000; intended max. amplitude
>    kenv    linen 1, .2,p3,.2; volume envelope
>    kfreq    
> =      cpspch(p4)
>    ibound  =      sr/4; 
> set it to sr/2 for true BL square wave
>    apulse  buzz 1, kfreq, ibound/kfreq, 1
>    asawdc integ apulse
>    asaw    
> =       asawdc - .5
>               out     asawdc*iamp*kenv
> endin
> 
> Indeed, if the fundamental period is 2pi and N the number of required
> harmonics (ibound/kfreq in instr 1), buzz opcode provides a 
> signal (assumely
> continuous)
> 
>                                   b(t) = (sum { cos(kt), k = 1.. N}) / N 
> 
> so, by integration, 
> 
>                             saw(t) = integ [b(u)du, u = 0..t]
>                             saw(t) = (sum { sin(kt) / k, k = 1.. N}) / N
> 
> which is precisely the reconstruction of the signal whose Fourier
> coefficients are (N times smaller than) (1,1/2,1/3,...,1/N) that 
> is just the
> asaw signal we're trying to build and I don't understand where 
> the 1/2
> offset comes from.
> 
> Is it a numerical (discrete signal) consequence ? If so, why 
> this 1/2
> coefficient doesn't depend of N (setting ibound to sr/2 for 
> example still
> requires the offset set to 1/2 to get the asaw expected).
> 
> Help me with my maths please!
> 
> 
> 
> --
> View this message in context: 
> http://csound.1045644.n5.nabble.com/unexpected-integ-offset-
> tp4827197p4827197.htmlSent from the Csound - General mailing 
> list archive at Nabble.com.
> 
> 
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> 

Dr Victor Lazzarini, Senior Lecturer, Dept. of Music,
National University of Ireland, Maynooth



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