% Analog Signal
Dt = 0.00005; t = -0.005:Dt:0.005; xa = exp(-1000*abs(t));

% Continuous-time Fourier Transform
Wmax = 2*pi*2000; 
K = 500; k = 0:1:K;                             % index array k for frequencies
W = k*Wmax/K;                                   % freqency between 0 and +pi, [0,pi] axis divided into 501 points.
Xa = xa * exp(-j*t‘*W) * Dt; 

magXa  = abs(Xa);  angXa  = angle(Xa);  realXa  = real(Xa);  imagXa  = imag(Xa);
%% --------------------------------------------------------------------
%%              START Xa‘s  mag ang real imag
%% --------------------------------------------------------------------
figure(‘NumberTitle‘, ‘off‘, ‘Name‘, ‘Example3.18 Xa its mag ang real imag‘);
set(gcf,‘Color‘,‘white‘); 
subplot(2,2,1); plot(W/pi,magXa); grid on;  %axis([0,1,0,1.5]); 
title(‘Magnitude Response‘);
xlabel(‘frequency in \pi units‘); ylabel(‘Magnitude  |Xa|‘); 
subplot(2,2,3); plot(W/pi, angXa/pi); grid on;  axis([-1,1,-1,1]);
title(‘Phase Response‘);
xlabel(‘frequency in \pi units‘); ylabel(‘Radians/\pi‘);

subplot(‘2,2,2‘); plot(W/pi, realXa); grid on;
title(‘Real Part‘);
xlabel(‘frequency in \pi units‘); ylabel(‘Real‘);
subplot(‘2,2,4‘); plot(W/pi, imagXa); grid on;
title(‘Imaginary Part‘);
xlabel(‘frequency in \pi units‘); ylabel(‘Imaginary‘);
%% -------------------------------------------------------------------
%%             END Xa‘s  mag ang real imag
%% -------------------------------------------------------------------



Xa = real(Xa);

W = [-fliplr(W), W(2:501)];                     % Omega from -Wmax to Wmax
Xa = [fliplr(Xa), Xa(2:501)];                   % Xa over -Wmax to Wmax interval

%% --------------------------------------------------------------------
%%              
%% --------------------------------------------------------------------
figure(‘NumberTitle‘, ‘off‘, ‘Name‘, ‘DSP MATLAB Example3.18‘);
set(gcf,‘Color‘,‘white‘); 
subplot(2,1,1); plot(t*1000,xa); grid on;  %axis([0,1,0,1.5]); 
title(‘Analog Signal‘);
xlabel(‘t in msec units.‘); ylabel(‘xa(t)‘); 
subplot(2,1,2); plot(W/(2*pi*1000), Xa*1000); grid on; % axis([-1,1,-1,1]);
title(‘Continuous-time Fourier Transform‘);
xlabel(‘frequency in KHz‘); ylabel(‘Xa(jW)*1000‘);

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%%           
%% -------------------------------------------------------------------