Fourier3

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Fourier3

  1. 1. Agung Budi Santoso, STSintesis Bentuk Gelombang & Spektrum Garis
  2. 2. SINTESIS BENTUK GELOMBANGSintesis (penyatuan) adalah gabungan dari bagian-bagian sehinggamembentuk satu kesatuan. Sintesis Fourier adalah penggabungankembali suku-suku deret trigonometri, lazimnya empat atau limasuku pertama agar menghasilkan gelombang mula-mula.
  3. 3. SPEKTRUM GARISSpektrum linier adalah sebuah kurva yang memperlihatkan masing-masing amplitudo harmonik di dalam gelombang. Garis-garisbertambah secara cepat pada gelombang-gelombang dengan deretyang mengecil (konvergen) secara cepat.Kandungan harmonik dan spektrum garis dari sebuah gelombangadalah bagian yang sangat alamiah dari gelombang tersebut dantidak pernah berubah, tanpa memperhatikan metode analisis.
  4. 4. %% Filename: example8.m%% Description: This M-file plots the truncated Fourier Series% for a square wave as well as its amplitude% spectrum.clear; % clear all variablesclf; % clear all figuresN = 11; % summation limit (use N odd)wo = pi; % fundamental frequency (rad/s)c0 = 0; % dc biast = -3:0.01:3; % declare time valuesfigure(1) % put first two plots on figure 1% Compute yce, the Fourier Series in complex exponential formyce = c0*ones(size(t)); % initialize yce to c0for n = -N:2:N, % loop over series index n cn = 2/(j*n*wo); % Fourier Series Coefficient yce = yce + cn*exp(j*n*wo*t); % Fourier Series computationendsubplot(2,1,1)plot([-3 -2 -2 -1 -1 0 0 1 1 2 2 3],... % plot original y(t) [-1 -1 1 1 -1 -1 1 1 -1 -1 1 1], :);hold;
  5. 5. plot(t,yce);grid;xlabel(t (seconds))ylabel(y(t));ttle = [EE341.01: Truncated Exponential Fourier Series with N = ,... num2str(N)];title(ttle);hold% Compute yt, the Fourier Series in trigonometric formyt = c0*ones(size(t)); % initialize yce to c0for n = 1:2:N, % loop over series index n cn = 2/(j*n*wo); % Fourier Series Coefficient yt = yt + 2*abs(cn)*cos(n*wo*t+angle(cn)); % Fourier Series computationendsubplot(2,1,2)plot([-3 -2 -2 -1 -1 0 0 1 1 2 2 3],... % plot original y(t) [-1 -1 1 1 -1 -1 1 1 -1 -1 1 1], :);hold;plot(t,yt);grid;xlabel(t (seconds))ylabel(y(t));ttle = [EE341.01: Truncated Trigonometric Fourier Series with N = ,... num2str(N)];title(ttle);hold
  6. 6. % Draw the amplitude spectrum from exponential Fourier Seriesfigure(2) % put next plots on figure 2subplot(2,1,1)stem(0,c0); % plot c0 at nwo = 0holdfor n = -N:2:N, % loop over series index n cn = 2/(j*n*wo); % Fourier Series Coefficient stem(n*wo,abs(cn)) % plot |cn| vs nwoendfor n = -N+1:2:N-1, % loop over even series index n cn = 0; % Fourier Series Coefficient stem(n*wo,abs(cn)*180/pi); % plot |cn| vs nwoendxlabel(w (rad/s))ylabel(|cn|)ttle = [EE341.01: Amplitude Spectrum with N = ,num2str(N)];title(ttle);hold
  7. 7. % Draw the phase spectrum from exponential Fourier Seriessubplot(2,1,2)stem(0,angle(c0)*180/pi); % plot angle of c0 at nwo = 0holdfor n = -N:2:N, % loop over odd series index n cn = 2/(j*n*wo); % Fourier Series Coefficient stem(n*wo,angle(cn)*180/pi); % plot |cn| vs nwoendfor n = -N+1:2:N-1, % loop over even series index n cn = 0; % Fourier Series Coefficient stem(n*wo,angle(cn)*180/pi); % plot |cn| vs nwoendxlabel(w (rad/s))ylabel(angle(cn) (degrees))ttle = [EE341.01: Phase Spectrum with N = ,num2str(N)];title(ttle);hold
  8. 8. EE341.01: Truncated Exponential Fourier Series with N = 11 2 1y(t) 0 -1 -2 -3 -2 -1 0 1 2 3 t (seconds) EE341.01: Truncated Trigonometric Fourier Series with N = 11 2 1y(t) 0 -1 -2 -3 -2 -1 0 1 2 3 t (seconds)
  9. 9. EE341.01: Amplitude Spectrum with N = 11 0.8 0.6 |cn| 0.4 0.2 0 -40 -30 -20 -10 0 10 20 30 40 w (rad/s) EE341.01: Phase Spectrum with N = 11 100angle(cn) (degrees) 50 0 -50 -100 -40 -30 -20 -10 0 10 20 30 40 w (rad/s)
  10. 10. KESIMETRISAN DALAM GELOMBANG PERIODIK1. SIMETRIS GENAP2. SIMETRIS GANJIL3. SIMETRIS GELOMBANG SETENGAH
  11. 11. SIMETRI GENAP
  12. 12. SIMETRI GANJIL
  13. 13. SIMETRI GELOMBANG SETENGAH
  14. 14. CONTOH SOAL

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