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07-14-2021
05:59 AM

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07-14-2021
05:59 AM

Fourier Amplitude Spectrum

Hello all,

I need help please with fourier analysis and the following problem:

- I can create my periodical time-signal f(t). --> Please see 1) and 2) in the attached file
- I also found the mathcad example from help menu for fourier analysis for calculating the fourier coefficients and plotting the graph. --> Please see 3a) in the attached file
- 1) For the following step I need a spectral analysis, means I need the amplitude spectrum and ideally a plot like this :

- 2) Afterwards I want to multiply the amplitude spectrum with an given impedance Z(s) to obtain the output voltage ripple

I hope you can help,

thanks in advance

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11 REPLIES 11

07-14-2021
07:13 AM

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07-14-2021
07:13 AM

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

07-14-2021
07:16 AM

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07-14-2021
07:16 AM

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:

Success!

Luc

07-14-2021
08:16 AM

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07-14-2021
07:14 PM

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07-14-2021
07:14 PM

07-14-2021
08:27 AM

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07-14-2021
08:27 AM

Can you please also attach a .pdf file? I have mathcad prime 3.0 and cannot open or convert your sheets 😞

07-14-2021
09:39 AM

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07-14-2021
09:39 AM

You should be able to open the attached.

Success!

Luc

07-14-2021
10:08 AM

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07-14-2021
10:08 AM

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?

07-14-2021
10:53 AM

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07-14-2021
10:53 AM

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:

07-14-2021
11:14 AM

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07-14-2021
11:14 AM

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).

07-14-2021
11:12 AM

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07-14-2021
11:12 AM

"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.

Success!

Luc

07-14-2021
07:39 PM

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07-14-2021
07:39 PM

Using FFT and IFFT, it requires 2^n data points to calculate.