# [R] Fast fourier transformation

baptiste auguie ba208 at exeter.ac.uk
Tue Feb 10 14:49:08 CET 2009

```A powerful scheme for harmonic inversion of time signals known as
"filter diagonalization method" is available from MIT: http://ab-initio.mit.edu/wiki/index.php/Harminv

I don't know of any R interface, but it might be a good option for

Cheers,

baptiste

On 10 Feb 2009, at 13:40, Dieter Menne wrote:

> 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
>
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> and provide commented, minimal, self-contained, reproducible code.

_____________________________

Baptiste Auguié

School of Physics
University of Exeter