Fast fourier transformation

botto <b.otto <at> uke.uni-hamburg.de> writes:

here is a practical problem we would like to solve. In a pneumatic post the
acceleration of the capsule is measured and plotted over time. From the
graph achieved we would like to derive some kind of statistic value that
describes the stress the capsule, or what is in it, is exhibited to.

..

1)      Apply a  fourier transformation to the acceleration profile to 

2)       get a number of harmonic waves describing my graph 

3)      and use the amplitudes of my waves in a weighted fashion to
calculate some statistical value.

What I tried to do is:

A)     construct an artificial profile fg for testing purpose like 

a.       f1 <- function(x) 0.5*sin(3*x + pi)

....

X)      in my test example I can define the amount of harmonic components,
because here I know that number. Of course afterwards in my natural profiles
I won't know.

Y)      I have to transform the values I get out of the "fft" and "fourier"
functions to estimate the frequency,  amplitude and phase of my harmonics.

Check function spectrum in stats which also has some methods to 
provide smoothed plots. There is also package signal which I have not
tried. And don't expect too much of phase plots, I have seen generations
of students jumping on these to explain the universum, the EEG  and US
politics because it sound so mysterious, and never seen a working method 
coming out of it.

It would have been good if you had provided a real example series because
then it would have been possible to tell you if you could find a reasonable
estimate of the "true" frequency and acceleration. In general, when you 
have only very few oscillations, you get a seemingly lousy estimate, which
is only the consequence of how fft is defined as a rather broad-minded
model. If you are sure that there is a single frequency with harmonics, 
other methods such as cyclic gams or even cyclic nlme (see the oestrus 
example in that package) might provide better results.

Dieter