Hi,

 

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.

 

The amount of stress introduced to the capsule will probably depend on two
things, the maximum amplitudes observed AND the frequency of these
amplitudes. A quick note at this point: Not the acceleration by itself but
the quick acceleration changes are the components which make up the special
stress we want to quantify.

 

So what I would like to do is: 

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)

b.      f2 <- function(x) sin(x + 0.75*pi)

c.       f3 <- function(x) 1.5*sin(0.45*x + 0*pi)

d.      fg <- function(x) f1(x) + f2(x) + f3(x)

B)      try to reconstruct the components of fg with  fft or fda.

 

What I don't understand yet is how:

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.

 

 

Is there a good function in these packages I can use for that?

 

Best regards,

 

Benjamin



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