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COMM 401: SIGNALS & SYSTEMS Lecture 10: Continuous Time Fourier Transfer

COMM 401: SIGNALS & SYSTEMS Lecture 10: Continuous Time Fourier Transfer. Dr.-Ing. Khaled Shawky Hassan Faculty of Information Engineering and Technology Khaled.shawky@guc.edu.eg. function sinc(t). clear; x_max=12 t = -x_max:2*x_max/1000:x_max; x=sinc(t); plot(t,x)

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COMM 401: SIGNALS & SYSTEMS Lecture 10: Continuous Time Fourier Transfer

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  1. COMM 401: SIGNALS & SYSTEMSLecture 10: Continuous Time Fourier Transfer Dr.-Ing. Khaled Shawky Hassan Faculty of Information Engineering and Technology Khaled.shawky@guc.edu.eg

  2. function sinc(t) clear; x_max=12 t = -x_max:2*x_max/1000:x_max; x=sinc(t); plot(t,x) v = [-x_max x_max -1.2*abs(min(x)) 1.2*max(abs(x))]; axis(v); title(['function sinc(t)']) xlabel('t') ylabel(['x(t)']) Dr.-Ing. Khaled Shawky Hassan Electronics and Electrical Engineering Department

  3. sinc(t) plot Dr.-Ing. Khaled Shawky Hassan Electronics and Electrical Engineering Department

  4. ak’s for rectangular pulse clear; %************** initial data *************** T=4; % period of the signal x(t) omega_0=2*pi/T; % fundamental frequency T_1=1; % half-width of the pulse K=T*3; % largest k for a_k k=-K:1:K; %************** a_k calculation *************** a_k = (2*T_1/T)*sinc(k*omega_0*T_1/pi); %*********** plot of a_k ************* clf stem(k,real(a_k)) v = [-K K -1.2*abs(min(a_k)) 1.2*max(abs(a_k))]; axis(v); title(['a_k for T_1=1 and T=',num2str(T)]) ylabel('Re\{a_k\}') xlabel('k') Dr.-Ing. Khaled Shawky Hassan Electronics and Electrical Engineering Department

  5. ak’s for rectangular pulse: plot Dr.-Ing. Khaled Shawky Hassan Electronics and Electrical Engineering Department

  6. ak’s for rectangular pulse: plot Dr.-Ing. Khaled Shawky Hassan Electronics and Electrical Engineering Department

  7. ak’s for rectangular pulse: plot Dr.-Ing. Khaled Shawky Hassan Electronics and Electrical Engineering Department

  8. ak’s for rectangular pulse: plot Dr.-Ing. Khaled Shawky Hassan Electronics and Electrical Engineering Department

  9. envelope of ak’s clear; omega_max=K*omega_0; omega = -omega_max:2*omega_max/1000:omega_max; x=2*(T_1/T)*sinc(omega*T_1/pi); plot(omega,x) v = [-omega_max omega_max -1.2*abs(min(x)) 1.2*max(abs(x))]; axis(v); title(['x=(2*T_1/T)*sinc(\omega*T_1/pi)']) xlabel('\omega') ylabel(['X(j\omega)/T']) Dr.-Ing. Khaled Shawky Hassan Electronics and Electrical Engineering Department

  10. envelope of ak’s Dr.-Ing. Khaled Shawky Hassan Electronics and Electrical Engineering Department

  11. frequency spectrum X(jw) clear; omega_max=K*omega_0; omega = -omega_max:2*omega_max/1000:omega_max; X=2*T_1*sinc(omega*T_1/pi); plot(omega,x) v = [-omega_max omega_max -1.2*abs(min(X)) 1.2*max(abs(X))]; axis(v); title([‘X=2*T_1*sinc(\omega*T_1/pi)']) xlabel('\omega') ylabel(['X(j\omega)']) Dr.-Ing. Khaled Shawky Hassan Electronics and Electrical Engineering Department

  12. envelope of ak’s Dr.-Ing. Khaled Shawky Hassan Electronics and Electrical Engineering Department

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