This is a Fourier waveform question that I am struggling with.

$$x(t) = \frac{8}{\pi}\left(\sin(8000\pi t)+ \frac{1}{3}\sin(24000\pi t) + \frac{1}{5}\sin(40000\pi t) + \frac{1}{7}\sin(56000\pi t) + \text{...} + \text{...}\right)$$

Updated with shown attempt.

F1 =2π/W1 =1/4000

F2 = 2π/W2 = 1/12000

F3 = 2π/W3 = 1/20000

F4 - 2π/W4 = 1/28000


F1/F2 = 3

F1/F3 = 5

F1/F4 = 7


35 X F1 = .00875 F0 = .00875

Fundamental frequency = 2π/F0 =360Hz

  • \$\begingroup\$ in format 1/Nsin(2πN f *t) f= 4kHz, N=1, then harmonic terms are 3f,5f,7f . No phase shift terms like a square wave \$\endgroup\$ Jan 2, 2020 at 13:46
  • \$\begingroup\$ Welcome to EE.SE! This appears to be a homework question. As such, you need to show us your work so far, and explain which part of the question you're having trouble with. For future reference: Homework questions on EE.SE enjoy/suffer a special treatment. We don't provide complete answers, we only provide hints or Socratic questions, and only when you have demonstrated sufficient effort of your own. Otherwise, we would be doing you a disservice, and getting swamped by homework questions at the same time. See also here. \$\endgroup\$
    – Dave Tweed
    Jan 2, 2020 at 14:41
  • \$\begingroup\$ Regarding the update: F1 =/= 2π / W1, but F1 = 2π * W1 \$\endgroup\$
    – Huisman
    Jan 3, 2020 at 8:46
  • \$\begingroup\$ @Huisman So I have made a mistake in getting F1, F2, F3 and F4? It should be 2π *8000 = F1? \$\endgroup\$ Jan 3, 2020 at 8:51
  • \$\begingroup\$ Yes, do also check Tony's first comment... \$\endgroup\$
    – Huisman
    Jan 3, 2020 at 8:54

1 Answer 1


As this is probably a homework problem, I don't want to give you the direct answer. However I suggest you look up the Fourier series of common waveforms and see if you can find a match. You could also make a plot of the waveform versus time and see if you recognize the shape (you only need to plot the first five terms or so).

  • 2
    \$\begingroup\$ Stop being such a square Barry ;) \$\endgroup\$
    – Sorenp
    Jan 2, 2020 at 13:41
  • 2
    \$\begingroup\$ @Sorenp I like your hint. It's odd. \$\endgroup\$
    – Huisman
    Jan 2, 2020 at 13:46

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