08-28-2017
It looks to me like you have a granularity problem. Four dots as a sample can fit a lot of functions, with intermediate datapoints from increased sampling rates you could then use fft to get good sine waves, for example.
You can code fft.c then call it using the system() function in awk. I think your awk supports that call.
A google for 'fft.c' got me 10 first page hits that looked respectably good. There are sites with an array of algorithmic variants to meet differing needs.
fft is gold standard for fitting data sampling output.
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IGAWK(1) Utility Commands IGAWK(1)
NAME
igawk - gawk with include files
SYNOPSIS
igawk [ all gawk options ] -f program-file [ -- ] file ...
igawk [ all gawk options ] [ -- ] program-text file ...
DESCRIPTION
Igawk is a simple shell script that adds the ability to have ``include files'' to gawk(1).
AWK programs for igawk are the same as for gawk, except that, in addition, you may have lines like
@include getopt.awk
in your program to include the file getopt.awk from either the current directory or one of the other directories in the search path.
OPTIONS
See gawk(1) for a full description of the AWK language and the options that gawk supports.
EXAMPLES
cat << EOF > test.awk
@include getopt.awk
BEGIN {
while (getopt(ARGC, ARGV, "am:q") != -1)
...
}
EOF
igawk -f test.awk
SEE ALSO
gawk(1)
Effective AWK Programming, Edition 1.0, published by the Free Software Foundation, 1995.
AUTHOR
Arnold Robbins (arnold@skeeve.com).
Free Software Foundation Nov 3 1999 IGAWK(1)