Why is my fourier transform graph so weird?

Ok, so I am trying to proof fourier transform properties for discrete signals using MATLAB.

I will try to proof all properties, but I started with reflection on time and time/frequency shift properties.

Here is one of my codes, if you you run it you will see some really weird graphics. I don't quite understand why they are not coming out as sinoids or whatever. And I have to use fft for this, even though its a dft.

% Creating a discrete signal xn

N=15; % total number of elements
L=10; % numers different then 0

xn=[ones(1,L),zeros(1,N-L)]; 

n = -5:length(xn)-6;

%rectangle, starting at -5, ends at 4

%Creating xn shifted

xn2=[ones( 1,L), zeros(1,N-L)]; 

n2=0:length(xn2)-1; 
% shifted it

%fourier transforms:

x = fft(xn); 

t = -5:length(xn)-6;

w = -5*2*pi/N:2*pi/N:((length(xn)-6)*2*pi/N);

% FT for shifted signal:

x2 = fft(xn2);
t2 = 0:1:length(xn2)-1;

w2 = 0:2*pi/N:((length(xn)-1)*2*pi/N);

% Plotting graphs:

subplot(3,2,1);stem(n,xn); title('Signal');xlabel('N');ylabel('x[N]');
subplot(3,2,2);stem(n2,xn2); title('Shifted Signal 5');xlabel('N');ylabel('x[N]');
subplot(3,2,3);plot(t,x);title('FT on original Signal');xlabel('N');ylabel('X(n)');
subplot(3,2,5);plot(w,x);title('FT on original Signal');xlabel('w');ylabel('X(jw)');
subplot(3,2,4);plot(t2,x2);title('FT on shifted Signal');xlabel('N');ylabel('X(n)');
subplot(3,2,6);plot(w2,x2);title('FT on shifted Signal');xlabel('w');ylabel('X(jw)');

[Image Analyst]

I tried to run it (copied and pasted) but it didn't run.

Undefined function or variable 'L'.
Error in test3 (line 5)
xn=[ones(1,L),zeros(1,N-L)];

Post code that we can run so you can get a quick answer. Make it easy for us. As it is, now you've wasted that chance because I probably won't look at it until tomorrow. In the meantime, read this: http://www.mathworks.com/matlabcentral/answers/13205-tutorial-how-to-format-your-question-with-markup

[Rafael]

Are you sure you copied everything?

L is 10; its defined right up there

[Image Analyst]

Now that you fixed the formatting, it's there. Before, you had it on the same line as "% total number of elements" which meant it was part of the comments.

[Daniel kiracofe]

Well, first thing, your calculation of t is probably not correct. You have this:

t = -5:length(xn)-6;

Why start at -5? That's where you started the time vector, but the frequency vector won't start there. For your given parameters, I think t should run from -7 to 7, not from -5 to 9. Similar logic applies for w.

Now let's talk about t2. Why is t2 different than t? t2 should be -7 to 7 as well. It's not clear to me why it should start at 0. When you shift the time of a signal, you do not shift its frequency content. Its the same.

Does that help?

[David Young]

You say: "I have to use fft for this, even though its [sic] a dft." The FFT is just an efficient implementation of the DFT, so that's not an issue.