A More Accurate Fourier Transform Files

ElyaEItfm is Copyright 
2015 Elya Courtney.

USAGE

Usage: ElyaEItfm infile outfile fmin fmax fstep [factor] [window] [ycol] [tmin] [tmax] [append_flag]
ElyaEItfm does a fourier transform on up to 1 million points using explicit integration
the first column in infile is time, the others are amplitude
the first column in outfile is frequency, second the amplitude spectrum, third is phase
fmin, fmax, and fstep specify range and step size in frequency
factor is a scaling factor by which to multiply output
window=0 for no windowing, window=1 or 2 for sin^window
ycol specifies which y column to use (column 2 in the file is the first y column, etc.)
tmin and tmax specify the ranges of data to include in transform
Append flag appends output (doesn't erase existing file)


SIMPLE EXAMPLE

ElyaEItfm cos10000.txt cos10000.tfm 0 140 0.01 0.2

will read the imput file cos10000.txt, compute a Fourier transform from 0 Hz to 140 Hz in frequency 
steps of 0.01 and write the output to the file cos10000.tfm.  

The 0.2 factor provides the proper normalization of 2/10, because the source file has a sampling window of 10 seconds.

cos10000.txt is a sampled waveform of a series of 5 cosine terms with amplitudes of 1, 2, 3, 4, and 5, frequencies that 
are multiples of 10, and phases of 0.1 radians.


EXAMPLE OF SHORT TIME FOURIER TRANSFORMS

ElyaEItfm cos10000.txt cos10000a.tfm 0 140 0.01 2.0 0 1 0.0 1.0
ElyaEItfm cos10000.txt cos10000b.tfm 0 140 0.01 2.0 0 1 1.0 2.0
ElyaEItfm cos10000.txt cos10000c.tfm 0 140 0.01 2.0 0 1 2.0 3.0
ElyaEItfm cos10000.txt cos10000d.tfm 0 140 0.01 2.0 0 1 3.0 4.0
ElyaEItfm cos10000.txt cos10000e.tfm 0 140 0.01 2.0 0 1 4.0 5.0

will compute the short time (1 second) Fourier transforms over 1 second intervals from 1 to 5.

The normalization factor is 2, since it is 2/1.0 where the intervals are each 1.0 second.


ElyaEItfm is free software; you can redistribute it and/or modify it under the terms of the
GNU General Public License as published by the Free Software Foundation; either version
2 of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY;
without even the implied warranty of MERCHANTABILITY or FITNESS FOR
A PARTICULAR PURPOSE. See the GNU General Public License for more details.
You can also find the GPL on the GNU web site.

In addition, we kindly ask you to acknowledge ElyaEItfm and its authors in any program
or publication in which you use FFTW. (You are not required to do so; it is up to your
common sense to decide whether you want to comply with this request or not.) For general
publications, we suggest referencing: Elya Courtney and Michael Courtney, 
“A More Accurate Fourier Transform,” with an anticipated publication date in 2015. 
Search at scholar.google.com for full citation.
Authors can be contacted at elyacourtney@gmail.com and Michael_Courtney@alum.mit.edu