# Laplace of a Periodic Function

1. May 14, 2005

### Brian Moughtin

I need to plot several cycles of the output response.

The waveform is sawtooth, starting at 0 and taking 1 second to peak at 10, returning to 0 in 1 second.

The transfer function is S/S+1

So far I've got

10/1-e^-2s ((1/s^2) - ( e^-s/s^2) - (e^-2s/s^2) as the Laplace Transform of the waveform but now I'm stuck !

Any pointers appreciated !

2. May 14, 2005

### OlderDan

Something is not right here. There are some parentheses missing in your expression for the Laplace Transform. If I just add one at the end, it looks like

$$\frac{{10}}{1} - e^{ - 2s} \left[ {\frac{1}{{s^2 }} - \frac{{e^{ - s} }}{{s^2 }} - \frac{{e^{ - 2s} }}{{s^2 }}} \right]$$

Now you say that you have a sawtooth waveform, but what you describe is not a sawtooth. A sawtooth would return abruptly to zero at t = 1 second. If it takes a second to return to zero you have a triangular waveform.

I cannot find a way to interpret what you have written for the transform that looks like the correct result for either of these waveforms. Both cases are done in this document

http://mmweb.cis.nctu.edu.tw/course/AM/chap5.pdf [Broken]

As for plotting the output, if you already know the waveform, why are you taking the transform? I assume it is because this is an exercise and you are supposed to be showing that the inverse transform of your Laplace Transform gets you back to the correct waveform. How do you go about doing the inverse tansform?

Last edited by a moderator: May 2, 2017
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