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Waveshaping with CSound

... Yet to be finished ...
The basic principle of waveshaping is this formula: sig = f(g(t)). The output signal (sig) is the result of a function (f) applied on the result of another function (g). The input for the latter function (g) is for example the time (t).
f() is called the transfer function
The output signal is clearly dependent on f(), g(), and - importantly - the amplitude of g(). Usually, the larger the amplitude of g(), the more the final signal is distorted.
The ingredients for waveshaping are table (or tablei), gen routine 13 and gen routine 4
basic.orc
sr      =       44100
kr      =       4410
ksmps   =       10
nchnls  =       2

;================================================================;
;                                                                ;
;               General Purpose Waveshaping Instrument           ;
;                                                                ;
;                                                                ;
;                Coded by Russell Pinkston - Univ. of Texas      ;


instr   1

  ihertz           = cpspch(p4)
  iamp             =        p5
  i_transfer_func  =         2
  i_normalize_func =         3
  
  kenv    linseg  0, .01, iamp, p3-.11, 1, .1, 0             ;overall amp envelope
  kctrl   linseg  0,p3/2,.999,p3/2,0
  aindex  oscili  kctrl/2,ihertz,1
  asignal tablei  .5+aindex,i_transfer_func,1
  knormal tablei  .5+kctrl, i_normalize_func ,1               ;amplitude normalization function
          outs    asignal*knormal*kenv, asignal*knormal*kenv
endin
basic.sco
;===============================================================
; =========  Score for General Purpose Waveshaping Instrument 
;
;
; This demonstrates the use of high partials, sometimes without
;   a fundamental, to get quasi-inharmonic spectra from waveshaping.
;===============================================================

f1      0 1025 10 1
; transfer function1: h0 h1 h2 h3 h4 h5 h6 h7 h8 h9 h10 h11 h12 h13 h14 h15 h16
f2     0 1025 13   1   1   -1   1  -.8  0  .6   0   0   0  .4   0   0   0   0   .1  -.2  -.3  .5

; normalizing function with midpoint bipolar offset:
f3     0       513     4       2       1

i1      0       4       5.00   10000
i1      +       4       5.02   10000
i1      +       4       5.04   10000
i1      +       4       5.05   10000
i1      +       4       5.07   10000
i1      +       4       5.09   10000
i1      +       4       5.11   10000
i1      +       4       6.00    .   

s
f0      1
s

; transfer function2:        h0  h1  h2  h3  h4  h5  h6 h7  h8  h9 h10 h11 h12 h13 h14 h15 h16
f2     0  1025 13      1  1   0   0   0 -.1   0  .3  0 -.5   0  .7   0 -.9   0   1   0  -1   0
; normalizing function with midpoint bipolar offset:
f3     0       513     4       2       1

i1      0       4       5.00   10000
i1      4       .       6.00    .   
i1      8       .       7.00    .

s
;f0      1
s

; transfer function3: h0 h1 h2 h3 h4 h5 h6 h7 h8 h9 h10 h11 h12 h13 h14 h15 h16
f2     0  1025 13 1 1 0  0  0  0  0  0  0 -1  0  1  0   0   -.1 0   .1  0   -.2
;                      h17 h18 h19 h20 h21 h22 h23
                       .3  0   -.7 0   .2  0   -.1
; normalizing function with midpoint bipolar offset:
f3     0       513     4       2       1

i1      0       4       5.00   10000
i1      4       .       5.06    .
i1      8       .       6.00    .

e

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