GEN04
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## GEN04

GEN04 — Generates a normalizing function.

## Description

This subroutine 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.

Example 1270. An example of the GEN04 routine.

    <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

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

f4 0 513 4 3 1 - AND its normalizing function with midpoint bipolar offset

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