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GEN04

Generates a normalizing function by examining the contents of an existing table.

Syntax

f  #  time  size  4  source#  sourcemode

Initialization

size -- number of points in the table. Should be power-of-2 plus 1. Must not exceed (except by 1) the size of the source table being examined; limited to just half that size if the sourcemode is of type offset (see below).

source # -- table number of stored function to be examined.

sourcemode -- a coded value, specifying how the source table is to be scanned to obtain the normalizing function. Zero indicates that the source is to be scanned from left to right. Non-zero indicates that the source has a bipolar structure; scanning will begin at the mid-point and progress outwards, looking at pairs of points equidistant from the center.

📝 Note

  • The normalizing function derives from the progressive absolute maxima of the source table being scanned. The new table is created left-to-right, with stored values equal to 1/(absolute maximum so far scanned). Stored values will thus begin with 1/(first value scanned), then get progressively smaller as new maxima are encountered. For a source table which is normalized (values <= 1), the derived values will range from 1/(first value scanned) down to 1. If the first value scanned is zero, that inverse will be set to 1.
  • The normalizing function from GEN04 is not itself normalized.
  • GEN04 is useful for scaling a table-derived signal so that it has a consistent peak amplitude. A particular application occurs in waveshaping when the carrier (or indexing) signal is less than full amplitude.

Examples

Here is a simple example of the GEN04 routine. It uses the files gen04.csd.

An example of the GEN04 routine.
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<CsoundSynthesizer>
<CsOptions>
; Select audio/midi flags here according to platform
-odac  ;;;realtime audio out
;-iadc    ;;;uncomment -iadc if realtime audio input is needed too
; For Non-realtime ouput leave only the line below:
; -o gen04.wav -W ;;; for file output any platform
</CsOptions>
<CsInstruments>

sr = 44100 
ksmps = 32 
nchnls = 2 
0dbfs  = 1 

gisine   ftgen 0, 0, 16384, 10, 1                                               ;sine wave

instr   1

ihertz = cpspch(p4)
ipkamp = p5
iwsfn  = p6                                                                     ;waveshaping function   
inmfn  = p7                                                                     ;normalization function                                                                 
agate   linen   1, .01, p3, .1                                                  ;overall amp envelope
kctrl   linen   .9, 2, p3, 2                                                    ;waveshaping index control
aindex  poscil  kctrl/2, ihertz, gisine                                         ;sine wave to be distorted
asignal tablei  .5+aindex, iwsfn, 1                                             ;waveshaping
knormal tablei  1/kctrl, inmfn , 1                                              ;amplitude normalization
        outs    asignal*knormal*ipkamp*agate, asignal*knormal*ipkamp*agate

endin
</CsInstruments>
<CsScore>
f1 0 64 21 6    ;Gaussian (random) distribution
f2 0 33 4 1 1   ;normalizing function with midpoint bipolar offset

s
;       st      dur     pch     amp   wsfn inmfn
i1      0       4      6.00    .7      1     2
i1      4       .      7.00    .
i1      8       .      8.00    .
;-------------------------------------------------------------------------------------
f3 0 1025 13 1 1 0 5 0 5 0 10   ;Chebyshev algorithm
f4 0 513 4 3 1                  ;normalizing function with midpoint bipolar offset
s
;       st      dur     pch     amp   wsfn inmfn
i1      0       4      6.00    .9      3     4
i1      4       .      7.00    .
i1      8       .      8.00    .
e
</CsScore>
</CsoundSynthesizer>

These are the diagrams of the waveforms of the GEN04 routines, as used in the example:

f1 0 64 21 6 - Gaussian (random) distribution
f1 0 64 21 6 - Gaussian (random) distribution
f2 0 33 4 1 1 - AND its normalizing function with midpoint bipolar offset
f2 0 33 4 1 1 - AND its normalizing function with midpoint bipolar offset
f3 0 1025 13 1 1 0 5 0 5 0 10 - Chebyshev algorithm
f3 0 1025 13 1 1 0 5 0 5 0 10 - Chebyshev algorithm
f4 0 513 4 3 1 - AND its normalizing function with midpoint bipolar offset
f4 0 513 4 3 1 - AND its normalizing function with midpoint bipolar offset