19-Tanzanite

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How can I extend a signal defined in a finite range to be periodic?

Forum|Forum|3 years ago
April 18, 2023
3 replies
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Hello,

????

How can I extend the above x(t,...) signal which is defined from -pi to pi to a periodic one so that I can display more periods of the signal, as it is shown below?

Mathcad Prime 8 file attached.

Thank you.

1_Untitled.zip

Calculus_Derivatives

Best answer by Werner_E

How can I extend the above x(t,...) signal which is defined from -pi to pi to a periodic one so that I can display more periods of the signal, as it is shown below?

If its just for displaying the graph, here are a few ways to turn a piece of a function periodic.

I created utility functions which expect a function with just one argument.

The first way uses the floor function

Another possibility would be to use the mod function. Because its implemented in Prime in a way to return negative values for negative arguments (which is undesirable here), I used it twice, adding the period for the second time to be sure to avoid negative values.

You may also use a recursive approach, but I would not suggest doing so

You could achieve the same effect as in the recursive approach by using a while loop

Attached sheet is in Prime 9 format

-

-MFra-

21-Topaz II

In the attached pdf, from page 12 onwards, there are numerous examples:

1_Fourier-series-of-forty-one-periodic-functions.pdf

C

Cornel

Author

19-Tanzanite

Ok. Thank you. But now I am interested in the extension of the periodicity to start from my function defined above (x(t,...)) and adapted in order to be able to display 2 periods, or 3 periods, etc.

T

terryhendicott

21-Topaz II

Hi,

To plot the periodic function try this:

To plot one or more periods restrict the variable t to a given range.

1_230418-Periodic.zip

W

Werner_E

Answer

25-Diamond I

How can I extend the above x(t,...) signal which is defined from -pi to pi to a periodic one so that I can display more periods of the signal, as it is shown below?

If its just for displaying the graph, here are a few ways to turn a piece of a function periodic.

I created utility functions which expect a function with just one argument.

The first way uses the floor function

Another possibility would be to use the mod function. Because its implemented in Prime in a way to return negative values for negative arguments (which is undesirable here), I used it twice, adding the period for the second time to be sure to avoid negative values.

You may also use a recursive approach, but I would not suggest doing so

You could achieve the same effect as in the recursive approach by using a while loop

Attached sheet is in Prime 9 format

1_Still-untitled.zip

C

Cornel

Author

19-Tanzanite

I do not have at this moment Mathcad Prime 9, but just Mathcad Prime 8. So, I cannot open Mathcad Prime 9 file. But I inserted the mkPer1 function you wrote.

a)

Here I do not know why signalp(t) shows these discontinuities.

b)

c)

Mathcad Prime 8 file attached.

1_Untitled-2.zip

W

Werner_E

25-Diamond I

@Cornel wrote:

I do not have at this moment Mathcad Prime 9, but just Mathcad Prime 8.

That was the reason for the pictures I attached 😉

Here I do not know why signalp(t) shows these discontinuities.

Actually the signal IS NOT continuous. The vertical line segments which you seem to be missing would be incorrect from a mathematical point of view. But Prime omits these lines not because its so clever as we can see in the other examples.

Actually I don't know how plotting is implemented, so we can tell when vertical lines would be plotted and when not.

In my original file the verticals were missing when I used the quickplot feature but, as you could see in the picture, they were plotted when I defined a range for the abscissa values t.

When I opened your sheet and defined a range, nothing changed - the vertical lines still were not plotted.

I also tried modifying your function definition, but as you can see in the next pic, the vertical lines are still missing partially for the periodic signalp(t), but it IS drawn in the plot of signal(t), The verticals are now drawn to connect the periodic parts, but not in the parts themselves. Can't explain why.

But then, the 2D plots in Prime have also other disadvantages and strange bugs (one is mentioned in my last picture). It sure isn't a masterpiece of programming.