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A
AS_98244341-Visitor
1-Visitor
March 1, 2021
Solved

Plot of complex numbers and symbolic engine not working

  • March 1, 2021
  • 1 reply
  • 3957 views

Hi all,

I am trying to plot the amplitude spectra( or Fourier transform) of a one cycle sine wave

i.e sin(t)*u(t)-u(t-2*pi), where u(t) represents a Heaviside function.

 

1-I found the Fourier transform of this using integration. However, when f(t) * e^..... is put in the symbolic arrow does not give any answer and merely states the same. When sin(t)*e^-1i*w*t is integrated the symbolic gives the correct answer but why does it not work when f(t) is used.

 

2-Second problem, I want to plot this fairly simple function. The problem is mathcad is saying the real part is around 0.075 according to the graph. It should be 0,0. The imaginary part should be 0,-3.141... however mathcad is plotting 1,-3.141.... What is going on?

The file is attached. Prime 6 was used

Best answer by Werner_E

The plot is correct, but the scaling which was automatically chosen by Prime is ... unfavorable, to keep it polite.

If you look closely you see that the point is right between -0.15 and +0.15, so its correctly at zero. The short vertical line you see from the point to the x.axis is drawn, because you had chosen a "Stem plot" as plot type for the real part instead of a normal "Line Trace".

Because of the scale chosen by Prime the axis in your plot don't cross at (0,0) even though the appropriate button is pressed. You can move the axis with the mouse, but it will only snap to an axis tick.
You have to manually change the scaling - its not obvious but you can edit the first, second and last value at each axis (the values highlighted in yellow in the picture below).
Primes plotting abilities are far away from being state of the art and the 3D-plots are even worse.

BTW, you may consider making w an additional argument of function f and use F(1) instead of defining w:=1 for the whole rest of the sheet.

Werner_E_0-1614671017868.png

 

 

1 reply

W
Werner_E25-Diamond I
25-Diamond I
March 1, 2021

Delete the definition of w:=1 at the top of the sheet and see if things are working as you expect.

 

BTW, you can use an omega instead of just w by typing w followed by Ctrl-g

A
AS_98244341-VisitorAuthor
1-Visitor
March 1, 2021

Hi,

I tried that but it doesn't work. It does give the correct symbolic result but now the graph is wrong. And when I do w:1 , the previously mentioned problem occurs. 

W
Werner_E25-Diamond I
25-Diamond I
March 1, 2021

When the symbolic result is correct, why do you think that the graph is wrong?

The real part is constant zero and the imaginary part is the hyperbola -pi/w

F(1)=0-3.14 *j

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