Hey, basically I have 32 data points that when graphed and joined to
each other make a complex wave. Now what I want is for to be able to
input these 32 data points into a program and for to get back as a
result, what are the dominant frequencies (simple waves) within this
program. Hopefully this is understandable. Anyways I am told that a
FFt program would do such a thing for me and so that is why it is 32
data points (2^8).

    So what I need is for someone to provide me with a program that
will do the following:
Take an input of a complex wave in the form of data points and with
this input determine the dominant simple waves within this complex
wave.


Just a quick note: I have looked around for a while on the net for
such programs and have found a few but I could never get them to work.
Basically this is because of my lack of programming skill most likely
(i.e non-existent). I had compiled the code for one or two but I could
never get them working properly.

Hopefully you will have better luck anyhow!

---

Clarification of Question by purpleh-ga on 06 Jan 2005 12:13 PST

Really, an answer on this before the 10th. Sorry for the tight deadline.

The Analysis ToolPak add-in that comes with Excel contains an FFT
analysis routine that you can use to solve this problem.

I tried using the Analysis ToolPak in Excel like you suggest and I
tried it on a simple sine wave and got back various values. All of
them were complex numbers except for the first number. Now I was kind
of wondering what precisely these numbers are telling me? Why is the
first value not the the same as the others? Is it because that is the
constant? Sorry for my understanding of Fft being abit limited.

The first number is the constant term in the series.  The subsequent
numbers are the coefficients for terms involving increasingly higher
frequencies.  You can think of the real part of these numbers as
corresponding to the coefficients of the cosine terms, while the
imaginary part correspond to the coefficients of the sine terms.  To
compare the magnitudes of the frequencies making up your composite
signal, you need to compare the magnitude of the complex coefficients.
 The magnitude of each frequency contribution is simply equal to the
square root of the sum of the squares of the real and imaginary parts.

The actual frequencies of the terms in the series are determined by
the total time represented by your data.  If your time series
corresponds to N = 32 samples taken at 1 sec intervals, then the total
duration of your sequence is T = 32 sec, and the terms in the
transform correspond to frequencies k*1/T, where k is an integer from
0 to (N/2-1) (i.e., the first number corresponds to the 0Hz
contribution, the second to 1/32 Hz, the next to 1/16 Hz, the next to
1/8 Hz, etc.).

Note that only half of the coefficients calculated by Excel are
meaningful because of a little complication known as the Nyquist
criterion, which says that for a sampling frequency T/N, one can only
obtain reliable frequency information only for frequencies less than
T/(2*N).  This is why k in the above paragraph only runs from 0 to
(N/2-1), and not from 0 to N.

Minor correction to what I wrote in my comment last night (it was late
<g>).  If you have 32 observations in your time series, each separated
by a time interval delta-T, then the total time represented by the
sequence is T = 31*delta-T (not 32*delta-T as I wrote in my comment). 
The frequencies of each term in the discrete Fourier series still
correspond to k*1/T, (k=0...N/2-1) but for the example I gave, T would
be 31 seconds, not 32 seconds.

Thanks alot man for all the help ye gave me! It was indispensable