【MATLAB】信号与系统 — 三角形脉冲信号的频谱

 clear all;

    
 clc;
    
 % f(t)
    
 tau = 4;
    
 t_vector = -4:0.01:4;
    
 N = length(t_vector);
    
 f_t = zeros(1,N);
    
 for n = 1:N
    
 t = t_vector(n);
    
 if (t>=-tau/2)&&(t<=tau/2)
    
 f_t(1,n) = 1 - (2/tau)*abs(t);
    
 end
    
 end
    
 figure; subplot(2,1,1);
    
 plot(t_vector,f_t,'b-');
    
 xlabel('t'); title('f(t)');
    
 axis([-4,4,-0.5,1.5]);
    
 grid on;
    
 % F(jw)=FT[f(t)]
    
 lower = - 15;
    
 upper = 15;
    
 step = (upper-lower)/100;
    
 w_vector = lower:step:upper;
    
 K = length(w_vector);
    
 X = zeros(1,K);
    
 for k = 1:K
    
 w = w_vector(k);
    
 % result from definition.
    
 f_t = @(t) (1-(2/tau)*abs(t)).*exp(-j*w*t);
    
 F_w(k) = quad(f_t,-tau/2,tau/2);
    
 % eq. (4.5-31)
    
 F_w_2(k) = (tau/2)*sinc(w*tau/(4*pi))^2;
    
 end
    
 subplot(2,1,2);
    
 plot(w_vector,abs(F_w),'r-');
    
 hold on;
    
 plot(w_vector,abs(F_w_2),'g:');
    
 legend('result from definition','eq. (4.5-31)');
    
 xlabel('\omega'); title('F(j\omega)');
    
 axis([lower,upper,-0.5,2.5]);
    
 grid on;
    
    
    
    
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