Fourier series and sketch the waveform

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SUMMARY

The discussion revolves around sketching a piecewise function defined by f(wt) = 0 for 0 ≤ ωwt ≤ π/2, f(wt) = Vsin(ωt) for π/2 ≤ ωwt ≤ π, f(wt) = 0 for π ≤ ωwt ≤ 3π/2, and f(wt) = Vsin(ωwt) for 3π/2 ≤ ωwt ≤ 2π. Participants emphasize the importance of accurately sketching the waveform, noting that transitions between segments should be vertical. The Fourier series coefficients, particularly a0, are discussed, with participants seeking clarification on integration methods and the implications of the function's symmetry.

PREREQUISITES
  • Understanding of piecewise functions and their graphical representation
  • Familiarity with Fourier series and Fourier coefficients
  • Knowledge of trigonometric functions, specifically sine functions
  • Basic integration techniques for calculating Fourier coefficients
NEXT STEPS
  • Study the process of deriving Fourier coefficients for piecewise functions
  • Learn about the convolution theorem in relation to Fourier transforms
  • Explore the implications of function symmetry on Fourier series
  • Practice sketching piecewise functions and identifying their periodic properties
USEFUL FOR

Students and educators in mathematics and engineering, particularly those focusing on signal processing, waveform analysis, and Fourier analysis.

  • #31
MattSiemens said:
Am I right in saying then gneill that there is no symmetry and that applying the rules for odd and even functions this proves that?
There is plenty of symmetry, just not the very simplest symmetry ##f(-x) = \pm f(x)##
 
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  • #32
MattSiemens said:
Am I right in saying then gneill that there is no symmetry and that applying the rules for odd and even functions this proves that?
I would agree that the test shows that the function is neither odd nor even.
 
  • #33
gneill said:
I would agree that the test shows that the function is neither odd nor even.
Thanks both gneil and BvU :-)
 
  • #34
Hi this is my first post please be gentle, I am on a track to answers to this question however my coefficient values seem different to this post and https://www.physicsforums.com/threads/fourier-series-of-a-waveform.766224/page-2#post-5143480.

Am I way off track with my understanding which I have attached for your attention.

Regards
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