Fourier 1 Hany Ferdinando Dept of Electrical Eng

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

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

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…! 3 Fourier (1) - Hany Ferdinando

Signal Representation n n 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. 4 Fourier (1) - Hany Ferdinando

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

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

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

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

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

Fourier in Electrical Engineering n Electronics ¡ ¡ ¡ Image and signal pre processing Convolution Electric circuit analysis for non DC signal 10 Fourier (1) - Hany Ferdinando

Fourier in Electrical Engineering n Telematics: ¡ ¡ ¡ Image and signal pre processing Modulation analysis Sampling analysis 11 Fourier (1) - Hany Ferdinando

Fourier Analysis n Fourier Series ¡ ¡ n n Exponential Sinusoid Fourier Transform Discrete-time Fourier Transform Discrete Fourier Transform (DFT) Fast Fourier Transform (FFT) 12 Fourier (1) - Hany Ferdinando

Fourier Series Exponential with 13 Fourier (1) - Hany Ferdinando

Fourier Series Sinusoids with 14 Fourier (1) - Hany Ferdinando

Exercise: n Get ao, an and bn for square wave below: 1 1 n 2 3 4 5 6 7 8 Get ao, an and bn for sawtooth wave below: 1 1 2 3 4 5 6 7 8 15 Fourier (1) - Hany Ferdinando

Electric Circuit Analysis n n n 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 16 Fourier (1) - Hany Ferdinando

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

Example. . . Calculate the voltage drop at the inductor!! 5 1 2 3 4 5 6 7 8 18 Fourier (1) - Hany Ferdinando

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 19 Fourier (1) - Hany Ferdinando