On Mon, 28 Jul 2014 14:06:18 +0000 (UTC), "adansteel "
<adansteel@libero.it> wrote:
>I would like to thank both of you very much for the fast replies.
>
>To overcome the problem of units redefinitions etc, I tried to use numerical integration algorithm: I simply wrote the definition of the fourier transform and I tried to compute numerically.
>
>the obtained data are in perfect agreement between numerical and theoretical in both cases (exp(-t) and exp(-2t).
>
>But, I would like to understand better what Charlie Roberts was saying about reading in the literature about the passage between dft and fourier transform, can you suggest a good source?
>
>thank you very much again.
Not much more that I can say than "read the literature"! Even simple
plotting software will tell you how to compare discrete computational
results with theoretical (integral based) results. That is why I
suggested you look at the histogram.
Here is a poser. Say you want to test the normal deviate routine
in Matlab. Okay, you use it to get 100,000 samples, for a
given mean and std. dev. Now, how are you going to see how
close it is to the real distribution? Well, you can plot a histogram
of your results and superpose the normal distribution you used to
get the deviates. But the histogram will depend on the bin width
you choose. So how to superpose the theoretical Gaussian on
your histogram. Clearly, the bid width plays a role, right? In the
same way, you have to account for the discrete sampling of the
frequency when you compare the DFT results to the theoretical
value.
I suggest you at least look into the chapter on FFTs in
'Numerical Receipes' for a start. See how the sampling
frequency comes into the game. But, any graphics software
package (PV Wave, Matlab, ... ) will, sooner or later, give
an example of how the compare the kind of things you have.
If you are mathematically inclined, you may want to think about
the measure of the variables you are comparing.
CR
<adansteel@libero.it> wrote:
>I would like to thank both of you very much for the fast replies.
>
>To overcome the problem of units redefinitions etc, I tried to use numerical integration algorithm: I simply wrote the definition of the fourier transform and I tried to compute numerically.
>
>the obtained data are in perfect agreement between numerical and theoretical in both cases (exp(-t) and exp(-2t).
>
>But, I would like to understand better what Charlie Roberts was saying about reading in the literature about the passage between dft and fourier transform, can you suggest a good source?
>
>thank you very much again.
Not much more that I can say than "read the literature"! Even simple
plotting software will tell you how to compare discrete computational
results with theoretical (integral based) results. That is why I
suggested you look at the histogram.
Here is a poser. Say you want to test the normal deviate routine
in Matlab. Okay, you use it to get 100,000 samples, for a
given mean and std. dev. Now, how are you going to see how
close it is to the real distribution? Well, you can plot a histogram
of your results and superpose the normal distribution you used to
get the deviates. But the histogram will depend on the bin width
you choose. So how to superpose the theoretical Gaussian on
your histogram. Clearly, the bid width plays a role, right? In the
same way, you have to account for the discrete sampling of the
frequency when you compare the DFT results to the theoretical
value.
I suggest you at least look into the chapter on FFTs in
'Numerical Receipes' for a start. See how the sampling
frequency comes into the game. But, any graphics software
package (PV Wave, Matlab, ... ) will, sooner or later, give
an example of how the compare the kind of things you have.
If you are mathematically inclined, you may want to think about
the measure of the variables you are comparing.
CR