%關於連續函式求傅立葉變換
%用有限長序列近似 原函式（利用e^-5 約為 0）
%從而確定出序列間隔T的範圍，接下來要確定T的步進量
%要求：步進T<<取樣間隔
%先求出傅立葉變換換後 幅值在什麼（設為f）頻率下趨向0
%步進T取一個值<<1/f\

%analog signal
dt = 0.00005;                                                       %時間步進量
t = -0.005:dt:0.005;                                              %時間範圍 
xa = exp(-1000*abs(t));                                        %求函式值
%contunites_time fourier transform
Wmax = 2*pi* 2000;                                             %觀察的最高頻率
K = 500;                                                               %500份頻率值
k = 0: 1: K;
W = k*Wmax/K;
Xa = xa * exp(-1i * t'*W)*dt;
Xa = real(Xa);
W = [-fliplr(W),W(2:501)];              %Flip matrix left to right  倒置 左右逐個交換
Xa = [fliplr(Xa),Xa(2:501)];            %xa over -Xa to Xa 合併矩陣
subplot(2,1,1);
plot(t*1000,xa);grid
title('analog signal');
xlabel('t  (ms)');
ylabel('xa(t)');
subplot(2,1,2);
plot(W/(2*pi*1000),Xa*1000);grid
title('continues_time fourier transform');
xlabel('f   (Khz)');
ylabel('Xa(jw) * 1000');

        %analog signal
dt = 0.00005;
t = -0.005: dt: 0.005;
xa = exp(-1000*abs(t));
        %discrete_time signal
ts = 0.0002;
n = -25:1:25;
x = exp(-1000*abs(n*ts));
        %discrete-fourier transform
K = 500;
k = 0:1:K;
w = 2*pi*k/K;
X = x*exp(-1i *n'*w);
X= real(X);
w = [-fliplr(w),w(2:K+1)];
X = [fliplr(X),X(2:K+1)];                                       %要對應-w所求的值
subplot(2,1,1);
        %hold on retains the current plot and certain axes properties so that
        %subsequent graphing commands add to the existing graph. If no
        %current axes exist before you call hold on, MATLAB creates new
        %axes and retains the default properties. However, some axes
        %properties change to accommodate additional graphics objects.
        %For example, the axes' limits increase when the data requires them
        %to do so. hold on sets the NextPlot property of the current figure and axes to add.
plot(t*1000,xa);
title('discrete signal');
xlabel('t in msec');
ylabel('x(n)');
hold on
        %stem(X,Y)     stem   Plot discrete sequence data
stem(n*ts*1000,x);
        %gtext   Mouse placement of text in 2-D view
        %gtext displays a text string in the current figure window after you select
        %a location with the mouse.
        %gtext('string')
        %hold      Retain current graph in figure
        %hold off resets axes properties to their defaults before drawing new
        %plots. hold off is the default. hold off sets the NextPlot property of the current axes to replace.
gtext('ts = 0.2msec'); hold off
subplot(2,1,2);
plot(w/pi, X);
title('discrete_time fourier transform');
xlabel('frequence in pi unit');
ylabel('X(w)');