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Fourier Amplitude Spectrum

xyz123
10-Marble

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 :

 xyz123_0-1626256296249.png

  • 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

 

 

 

 

 

20 REPLIES 20
Werner_E
24-Ruby IV
(To:xyz123)

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.

Werner_E_0-1626262626434.png

EDIT: Forgot a minus sign in first place - is fixed now

Prime 6 sheet attached

LucMeekes
23-Emerald I
(To:xyz123)

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:

LucMeekes_1-1626261344078.png

for all values of n in your range (1 to Nt). The magnitudes Mn are calculated from the corresponding values of A and B:

LucMeekes_3-1626261389284.png

Success!

Luc

 

ttokoro
17-Peridot
(To:xyz123)

image.png

ttokoro
17-Peridot
(To:ttokoro)

image.png

xyz123
10-Marble
(To:xyz123)

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

LucMeekes
23-Emerald I
(To:xyz123)

You should be able to open the attached.

 

Success!
Luc

xyz123
10-Marble
(To:xyz123)

Unfortunately no, I cant open it... 😞  It´s not compatible and also I cannot convert it. Hmmm ?!

xyz123_0-1626271310280.png

 

Anyway, here is the result from the support from Luc and Werner so far:

 

xyz123_1-1626271421039.png

 

How do I obtain the same discrete plot like Werner and ttokoro?

 

 

Werner_E
24-Ruby IV
(To:xyz123)

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

Werner_E_0-1626274064926.png

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:

Werner_E_1-1626274744160.png

 

Werner_E
24-Ruby IV
(To:Werner_E)

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).

LucMeekes
23-Emerald I
(To:xyz123)

"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

 

ttokoro
17-Peridot
(To:xyz123)

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

image.png

xyz123
10-Marble
(To:ttokoro)

Great, thank you ttokoro,

 

thank you for the advice with the FFT and IFFT command. I will investigate further!

 

Best regards 

xyz123
10-Marble
(To:xyz123)

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:

 

xyz123_0-1628065761350.png

 

Next step, my output impedance as an example:

 

xyz123_2-1628066039660.png

 

Next step, output voltage:

 

xyz123_3-1628066096411.png

 

Next step: Obtaining Output voltage without DC part. Should be fine:

 

xyz123_4-1628066190196.png

 

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

 

 Best regards!

 

LucMeekes
23-Emerald I
(To:xyz123)

What is the objective:

1. To get the resulting output voltage.

(Which would be:

LucMeekes_0-1628084333103.pngfor the three periods)

or

2. To learn Fourier transforms

 

You should be more careful about the impedance. If it is given as:

LucMeekes_0-1628082576874.png

You cannot simply change the parameter s to f:

LucMeekes_1-1628082604961.png

Because s is a complex number. Taking the absolute value of the result becomes ridiculous, because now all your numbers are real:

LucMeekes_2-1628082705049.pngLucMeekes_3-1628082721582.png

With, a Z(s) defined as:

LucMeekes_4-1628082772768.png

You get:

LucMeekes_5-1628082795933.png

LucMeekes_6-1628082810764.png

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:

LucMeekes_7-1628083655046.png

Then you should be able to plot:

LucMeekes_8-1628083699770.png

versus tx.

But first correctly use your impedance.

 

Success!
Luc

 

ttokoro
17-Peridot
(To:xyz123)

image.pngimage.pngimage.png

image.png

ttokoro_0-1628118835160.png

 

If the output is voltage, high frequency short the capacitor and Ztotal becomes 50 mΩ. That is V=IZ=I/20 as shown in my results.  

ttokoro
17-Peridot
(To:ttokoro)

If the current has the period image.png, then Ztotal becomes 2 ohm at 100 Hz. Then the result should be  image.pngimage.png

-MFra-
21-Topaz I
(To:xyz123)

Hi,

you might be interested in this work of mine made years ago on the subject:

Waverorm Spectra.jpg

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.

CornelBejan
15-Moonstone
(To:-MFra-)

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.

The original files for M15 I published some time ago in the community, just search (Fourier Analysis) and download them.

-MFra-
21-Topaz I
(To:-MFra-)

You might also be interested in this other work of mine from years ago:

Digital filters equivalent to linear classics.jpg

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