1. Fourier Series

2. Fourier Series
is the “fundamental frequency”

3. Fourier Series
is the “fundamental frequency”

4. Fourier Series
Integration limits: when
, then
so we get:

5. Fourier Series
Euler:

6. Fourier Series
We can show ;
recall that

7. Phasors:
Phasors

8. Symmetry
Odd f(-t) =-f(t)
Fourier: sine terms only
Even f(t) = f(-t)
Fourier: cosine terms only
Neither

9. Half-wave symmetry:
has no even harmonics
| |
t t+T/2

10. Example of non-symmetric waveform:

11. Fundamental Signals
Unit Step:

12. Fundamental Signals
Unit Step:
Unit Impulse