what does the notation ( ' ) in the time sample t = (0:dt:0.002-dt) ' mean ??and thanks in advance

   Fs = 800e3;
   dt = 1/Fs;
   t =  (0:dt:0.002-dt)';
   Fm = 5000;
   y = cos(2*pi*Fm*t);
   figure;
   plot(t,y);

Answer 1

[Wayne King]

It is just making a column vector out of your time instants so that the resulting sine wave is also a column vector.

The above example would work equally well without the ', the only difference being that t and y would be row vectors

   Fs = 800e3;
   dt = 1/Fs;
   t =  (0:dt:0.002-dt);
   Fm = 5000;
   y = cos(2*pi*Fm*t);
   figure;
   plot(t,y);

However, further processing might be made easier by having a column vector.

[abdalrahman elhaw]

ok,but why the spectrum is not correct if i wrote time sample as t = (0:dt:0.002-dt);

Answer 2

[Wayne King]

What makes you say the spectrum is not correct?

Fs = 800e3;
dt = 1/Fs;
t =  (0:dt:0.002-dt);
Fm = 5000;
y = cos(2*pi*Fm*t);
ydft = fft(y);
ydft = ydft(1:length(y)/2+1);
df = Fs/length(y);
freqvec = 0:df:Fs/2;
plot(freqvec,abs(ydft))

It is exactly what I would expect.

[abdalrahman elhaw]

sorry , i mean this code how Fequency sample is written and why row vector is different from colum vector as they both generate the same values

Fs = 1000;                      
Ts = 1/Fs;                           
t =( 0:Ts:1-Ts)';
N = size(t,1);
B  =input('modulation index=');
Fm =input('signal frequency=');
Fc =input('carrier frequency=');                      
x = cos(2*pi*Fc*t+(B*sin(2*pi*Fm*t)));
figure;
plot(t,x);
xlabel('Time');
ylabel('Amplitude');
title('Modulated Signal');  
X = fftshift(fft(x));
dF = Fs/N;                      
f  = -Fs/2:dF:Fs/2-dF;
figure;
plot(f,abs(X));
xlabel('Frequency (in kHZ)');
title('spectrum of FM');

[Wayne King]

Well for one thing I see in the above you have the sampling frequency set to 1000 Hz. I don't know what values you eventually provide for all your input() statements, but I see from your xlabel() in kHz that you are way undersampling the signal -- you are going to alias the output. You can't have a carrier frequency in the kHz range when the sampling frequency is only 1 kHz.

[abdalrahman elhaw]

thanks for replying, but waht about the frequency vector ?i do not understand why it is in this form f = -Fs/2:dF:Fs/2-dF;

[Wayne King]

because you have called fftshift which centers the DC component in the middle so the spectrum runs from -Fs/2 to Fs/2 in increments of df

[abdalrahman elhaw]

OK,Why not writing it like Fs/2:dF:Fs/2;