Finding average slope using Fourier

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    Average Fourier Slope
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SUMMARY

This discussion focuses on calculating the average slope of a sawtooth waveform derived from a Fourier transform involving four sine waves. The user initially considers using the algebraic method of (y2-y1)/(x2-x1) for each waveform to find the average slope. However, there is a concern that integrating the waveform may yield a result of zero, leading to confusion about the definition of "average slope." The conversation emphasizes the importance of clearly defining the term to proceed effectively.

PREREQUISITES
  • Understanding of Fourier transforms and their application in waveform analysis.
  • Knowledge of calculus, specifically integration and differentiation techniques.
  • Familiarity with the concept of average slope in mathematical terms.
  • Experience with waveform generation and analysis, particularly sawtooth waveforms.
NEXT STEPS
  • Research the mathematical definition of "average slope" in the context of waveforms.
  • Explore integration techniques for periodic functions, particularly for sawtooth waveforms.
  • Learn about the implications of using Fourier series in waveform analysis.
  • Investigate numerical methods for approximating slopes in complex waveforms.
USEFUL FOR

Mathematicians, signal processing engineers, and anyone involved in waveform analysis or Fourier transform applications will benefit from this discussion.

dlesswater
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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.
 
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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.
 

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