Finding average slope using Fourier

[dlesswater]

I am working on a project in which we get the derivative of a sawtooth waveform as our output. I am having trouble deciding how I should go about finding the average slope of that waveform. We used a Fourier transform to construct the wave so I have the amplitude and phase relationships of 4 sine waves. I though about doing it algebraically (y2-y1)/(x2-x1) for each waveform then taking that average. The idea was proposed thought that I integrate the waveform but the problem is I believe this will give me zero. If anyone has any input on how it could be done with integration that would be greatly appreciated.

 

[fresh_42]

Guess you will have to define "average slope" first! And the answer will depend on this definition. Otherwise it's only guesswork what we can do here.