I need help please with fourier analysis and the following problem:
I hope you can help,
thanks in advance
This should help in plotting the spectra
Note that the vectorization I applied in the calculations of the amplitudes and phases is not mandatory in this case but good habit, as we are dealing with vectors and want the calcs being done element-wise.
EDIT: Forgot a minus sign in first place - is fixed now
Prime 6 sheet attached
You have the Fourier representation of your signal as a summation of sin and cos terms in Abschnitt 3). The arguments to the sin and cos can be rewritten as n*pi*t/L = 2*pi*f*t where f is the frequency you are looking for. This means that your f values are:
for all values of n in your range (1 to Nt). The magnitudes Mn are calculated from the corresponding values of A and B:
Unfortunately no, I cant open it... 😞 It´s not compatible and also I cannot convert it. Hmmm ?!
Anyway, here is the result from the support from Luc and Werner so far:
How do I obtain the same discrete plot like Werner and ttokoro?
It wasn't sure to which posting you were replying to. The use of the new and IMHO obsolete "Reply to topic" option at the end of each thread creates a reply to the very first, initial post of yourself.
Actually a pdf of my sheet would not show anything more than what can be seen in the picture I posted. There was nothing omitted and as I can see you were able to duplicate it.
The get the stem plot shown by me and ttokoro you have to use the "Change Type" Button from the menu and chose "Stem Trace"
Mit deutschem Menü: Diagramme - Typ ändern - Stammdiagramm
You should also know that you can change the first (lowest), second and last scale value for each axis. This is often necessary as the automatic scaling produces undesired steps and scale values. Because of the tiny font you may have a hard time selecting those values, though.
You can also move the axis around and for some reason in my amplitude plot the axis did not cross at 0;0. It should rather have looked like this:
I still can't read Prime 7 files but I opened ttokoros file converted by Luc with Prime 6 and created a pdf. It may contain some formatting glitches but I guess the vital information should be all there. ttokoro did not made use of the Fourier series but rather used the built-in discrete Fourier transform (dft) and its inverse (idft).
"Unfortunately no, I cant open it... "
That's weird. I can open the Files that I attached in my reply with Prime 2, then they should open in Prime 3 without problem.
You've probably selected the wrong file to open: the original file from Werner.
Please download the files that I attached (if necessary overwriting the files with the same name). Then open them with your Prime 3.
" I cannot convert it. "
Indeed, you cannot because you haven't installed Prime 7. But even then to convert them is a tedious task.
Okay, I have worked a little bit further on this topic and it should be almost completly finished now.
Thanks for the help guys!
So far so good, The amplitude spectrum looks now like this:
Next step, my output impedance as an example:
Next step, output voltage:
Next step: Obtaining Output voltage without DC part. Should be fine:
Last part what is needed:
Can you help to inverse transform the Voutpp amplitude spectrum to time domain?
I would like to plot the voltage (vout vs time) without the DC part
What is the objective:
1. To get the resulting output voltage.
(Which would be:
for the three periods)
2. To learn Fourier transforms
You should be more careful about the impedance. If it is given as:
You cannot simply change the parameter s to f:
Because s is a complex number. Taking the absolute value of the result becomes ridiculous, because now all your numbers are real:
With, a Z(s) defined as:
That's quite different from your result. This is important since you are going to use that impedance in further calculations.
Now to the inverse Fourier. You have the amplitudes of the (co)sine waves at each of the frequencies fk[i. All that should remain is adding those (co)sines. I'd guess something like:
Then you should be able to plot:
But first correctly use your impedance.
you might be interested in this work of mine made years ago on the subject:
The first seventy pages show the algorithms used and the signals with graphs, the spectra of which will be produced from page 72 onwards.
The original files for M15 were published some time ago in the community, just search and download them.
Can you attach a Mathcad file with this?
It would be good to post somewhere all these things that you have done in the past, both pdf and Mathcad files. Maybe some will help.