I will do my best to explain my problem clearly.  I have this same problem
using Labview, Matlab, and Scilab.  

I start by building an array with three frequencies (f1,f2,and f3) starting at
different times.  f1 for .5 seconds, f2 for .25 seconds, and f3 for .25 seconds.
 So, I have one second worth of data consisting of three frequencies that are at
different times. 

Then, I do an FFT of this data and get my results.  f1 has a higher magnitude
than f2 and f3.  One can make out the frequency content (for the most part);
however, from the FFT results, one can't tell which frequencies started at what
times.  Ok, fine.  I understand this so far.  

BUT!  What happens when you do an IFFT on this set of data?  I would anticipate
that I'd get some waveform with all three frequencies combined - NOT a result
that displays them in their original order.  But, that is exactly what I am
seeing - the same time-domain data I started with.  

I have also tried this by switching the order of f1,f2, and f3.  And, I also did
this with zero-stuffing three sets of data at different places.  Meaning, each
set of data had the same portion of data in it; however, at different locations.
 (For example, for 1000 points, let's say 100 of them contained data for 3
periods of a sine wave.  For set 1, the first 100 points were used for this
data.  For set 2, 300-400 were used for this data.  For set 3, 700-800 were
used.)  Then, I run an FFT on each set and then average the FFT results.  I then
run an IFFT on the averaged FFT results and end up the sum of the time-domain
signals.  ?!?!?!  

How is the IFFT able to identify the times at which these signals took place?  

And, finally, I ran a two chirps.  One chirp starting at f4 and ending at f5. 
The second chirp starts at f5 and ends at f4.  I then run FFT's on each of these
and get the same results.  Ok...  But, the IFFT of these results give me the the
same chirps I started with?  

I am really clueless why this is working.  The only explanation would be
computation mehtods.  But, I even saved the FFT results to a file, completely
closed out of that program, opened another program, and used the FFT results to
run an IFFT and got the same time-domain chirp back!  I am really confused.  Any
help is appreciated.  I hope this is somewhat clear.  Let me know if I need to
clarify anything.  

Undergrad Student,
Dave  

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