Plotting an Exponential Fourier Series

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SUMMARY

The discussion focuses on determining the phase angle of an exponential Fourier series. The user successfully calculates the coefficients and amplitude using the formula |Dn| = Cn/2. To find the phase angle, it is confirmed that the user must expand Cn into its real and imaginary components and apply the formula ø = ∠Dn, specifically using tan-1(-bn/an) for calculation. This method aligns with traditional approaches for sine and cosine expansions.

PREREQUISITES
  • Understanding of exponential Fourier series
  • Familiarity with complex numbers and their representation
  • Knowledge of trigonometric functions and their inverses
  • Experience with signal processing concepts
NEXT STEPS
  • Study the derivation of exponential Fourier series coefficients
  • Learn about the relationship between complex exponentials and trigonometric functions
  • Explore applications of Fourier series in signal analysis
  • Investigate the implications of phase shifts in signal processing
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Students and professionals in electrical engineering, signal processing, and applied mathematics who are working with Fourier analysis and need to understand phase determination in exponential Fourier series.

polaris90
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I'm having some problem in determining the phase of an exponential Fourier series. I know how to determine the coefficient which in turn gives me the series after I multiply by e^-(jωt)
I can determine the amplitude by dividing the coefficient by 2 |Dn| = Cn/2
Now my question is how to determine the phase angle. My book only gives me ø=∠Dn and it doesn't explain how they get the values. Do I have to expand Cn into its real and imaginary parts and then calculate the angle using tan-1(-bn/an) as I would when using sines and cosines?
 
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polaris90 said:
Do I have to expand Cn into its real and imaginary parts and then calculate the angle using tan-1(-bn/an) as I would when using sines and cosines?
Yes.
 

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