1. Fourier (1) Hany Ferdinando Dept. of Electrical Eng. Petra Christian University

2. Fourier (1) - Hany Ferdinando2 Overview History Signal representation Fourier in electrical engineering Fourier Series Application in electric circuit analysis

3. Fourier (1) - Hany Ferdinando3 History Jean Baptiste Joseph Fourier was born on March 21, 1768, in France He presented his paper about heat diffusion in 1807. He found series of harmonically related sinusoids to be useful in representing the temperature distribution through body But… no one accept his theory…!

4. Fourier (1) - Hany Ferdinando4 Signal Representation A periodic signal can be represented as sum of sinusoidal waves The sinusoidal wave has fundamental frequency and all waves are multiplication of that fundamental freq.

5. Fourier (1) - Hany Ferdinando5 Signal Representation Fundamental frequency = 50Hz, n = 1:10

6. Fourier (1) - Hany Ferdinando6 Signal Representation Signal in frequency domain

7. Fourier (1) - Hany Ferdinando7 Signal Representation Fundamental frequency = 50Hz, n = 1:10, amplitude is half of the previous signal

8. Fourier (1) - Hany Ferdinando8 Signal Representation Signal in frequency domain, see the amplitude!!

9. Fourier (1) - Hany Ferdinando9 Fourier in Electrical Engineering Power system:  To analyze the high freq. in the power line due to non linear load  power factor and power quality issue

10. Fourier (1) - Hany Ferdinando10 Fourier in Electrical Engineering Electronics  Image and signal pre processing  Convolution  Electric circuit analysis for non DC signal

11. Fourier (1) - Hany Ferdinando11 Fourier in Electrical Engineering Telematics:  Image and signal pre processing  Modulation analysis  Sampling analysis

12. Fourier (1) - Hany Ferdinando12 Fourier Analysis Fourier Series  Exponential  Sinusoid Fourier Transform Discrete-time Fourier Transform Discrete Fourier Transform (DFT) Fast Fourier Transform (FFT)

13. Fourier (1) - Hany Ferdinando13 Fourier Series Exponential with

14. Fourier (1) - Hany Ferdinando14 Fourier Series Sinusoids with

15. Fourier (1) - Hany Ferdinando15 Exercise: Get a o, a n and b n for square wave below: Get a o, a n and b n for sawtooth wave below: 12345678 1 12345678 1

16. Fourier (1) - Hany Ferdinando16 Electric Circuit Analysis For electric circuit with non DC source, we can use Fourier analysis to solve the circuit The source should be periodic, then we will use Fourier series Usually, the sinusoid formula is used

17. Fourier (1) - Hany Ferdinando17 Electric Circuit Analysis 1. Find the a o, a n and b n of all sources in the circuit 2. Find  of the signal (it is expressed in term of ‘n’) and transform all components into phasor representation 3. Get the equation and solve it (the solutions are in term of ‘n’)

18. Fourier (1) - Hany Ferdinando18 Example... 12345678 5 Calculate the voltage drop at the inductor!!

19. Fourier (1) - Hany Ferdinando19 Next… The Fourier Series is discussed and students have to exercise how to use it. For the next class, students have to read Fourier Transform: Signals and Systems by A. V. Oppeneim ch 4 and 5, or Signals and Linear Systems by Robert A. Gabel ch 5, or Sinyal & Sistem (terj) ch 4 and 5