# I am trying to run a code that results in AM. But in the frequency spectrum, I get the spectrum at a carrier frequency 6 times the original. What am i doing wrong?

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Jenny on 17 Oct 2013
Commented: David on 20 Oct 2013
fs=input('Input the sampling frequency : ');
fc=input('Input the carrier frequency : ');
fm=input('Input the message frequency : ');
Am=input('Input the message amplitude : ');
Ac=input('Input the carrier amplitude : ');
dt=1/fs;
t=[-3:dt:3];
m=Am*cos(2*pi*fm*t);
f=1./t;
M=ammod(m,fc,fs,0,Ac);
subplot(2,1,1)
plot(abs(fft(M)));
hold
subplot(2,1,2)
plot(t,M);
Navan Ruthramoorthy on 18 Oct 2013
What are the values you used when you tried? Can you post code with all the values for fs, fc etc plugged in instead of using input?
Jenny on 20 Oct 2013
Ok. Here it is -
fs=10000;
fc=1000;
fm=10;
Am=1;
Ac=10;
dt=1/fs;
t=[-3:dt:3];
m=Am*cos(2*pi*fm*t);
f=1./t;
M=ammod(m,fc,fs,0,Ac);
subplot(2,1,1)
plot(abs(fft(M)));
hold
subplot(2,1,2)
plot(t,M);

David on 20 Oct 2013
Edited: David on 20 Oct 2013
Are you remembering to divide by 2*pi in your frequency plot?? w = 2*pi*f and 2*pi~6.
If this isn't the problem then it may be the number of FFT points you are using. NFFTPts = (Fs*(max(T) - min(T)))/2.
Jenny on 20 Oct 2013
Edited: Jenny on 20 Oct 2013
I did forget to multiply 2*pi*f. But while doing so, i get 6283.18 rad/s. Whereas, what i get in the frequency spectrum is ~6000, like you said. But this difference in values, is it acceptable?(Im quite new to the subject of communication systems and the use of matlab)
When i applied 'NFFTPts = (Fs*(max(T) - min(T)))/2', Im getting the frequency as ~3000 rad/s.
David on 20 Oct 2013
Edited: David on 20 Oct 2013
Okay, since I do not know exactly how you are using the FFT function, a division of 2 may or may not be valid.
As for the slight differences you are getting in frequency, that might be due to the frequency resolution of your plot. Frequency resolution is given by the following equation:
df = 1/T = Fs/N
where T is total acquisition time, N is the number of samples, and Fs is the sampliing frequency. However, in your case, this would be df = 1/6 Hz, which is much smaller than the error you are getting. I'm not sure why you are getting these mixed results...
Note: The frequency resolution improves as the observation time T increases.