MATLAB: Coding FM modulation

fm modulation

|hi,

I'm writing FM modulation according the plain math (without any matlab functions): http://www.st-andrews.ac.uk/~jcgl/Scots_Guide/RadCom/part12/page1.html

http://en.wikipedia.org/wiki/Frequency_modulation

Fs = 100e3; % Sampling frequency for audio
dt = 1/Fs;   %to reduce number of elements in the vector and increase 
  %             calaulation time.
T = 1;
%t = 0:dt:T/2;
t = (0:Fs-1)/Fs;
df = 1/T;
Fmax = 1/2/dt;
f = -Fmax:df:Fmax-1;
% Carrier
fc = 10e3;
% Information - Time domain
fm = 200;   %in Hz
Am = 1;
Kp = 7.5;    
ym = Am*sin(2*pi*fm.*t);
deltaF = Kp*Am;
% Modulation
beta = deltaF/(fm);
y = 4*cos(2*pi*fc.*t+beta*sin(2*pi*fm.*t));
% Frequency domain
Y = fftshift(fft(y))/length(y);  
% Plots - Time domain
figure(1);
subplot(211), plot(t,cos(2*pi*fm.*t)),axis([0.21 0.221 -1.5 1.5]), grid on;
subplot(212), plot(t,y), axis([0.21 0.221 -5 5]), grid on;
% Plots - frequency domain
figure(2);
plot(f,10*log10(abs(Y))), grid on;
%end code

Only at very high values of Kp I'm getting correct results in time domain but in frequency i'm still not getting correct results.

Please help.

Best Answer

Hello Walter,

Thank you for the comment. I actually asked more on the FM modulation coding and incorrect outputs that get. Can you comment on that matter?

Thanks,

Related Solutions

MATLAB: Spectrum of fm modulaton

Hello AbdAlla, The generation of a real fm signal is not a linear process, but there is no problem with finding the resulting spectrum by fft since the fft can find the frequency components of any signal. The fft works out best with modulation by a tone or the sum of a small number of tones, AND when the carrier and all the tones have an exact number of cycles in the time array.

(revised) Here is a small example:

F = 1e6;                 % sampling frequency
f0 = 20000;              % carrier
f1 = 200;                % modulating tone
beta = 1;                % modulation index  
% signal, spectrum
N = 1e6;
t = (0:N-1)*(1/F);       % delt = 1us
y = cos(2*pi*f0*t+beta*cos(2*pi*f1*t));
z = fftshift(fft(y))/N;
f = (-N/2:N/2-1)*(F/N);
% predicted sidebands for the positive frequencies only
n = 4;
sidamp = (1/2)*besselj(0:n,beta);
sidamp = [fliplr(sidamp(2:end)), sidamp];
sidf = (f0-n*f1):f1:(f0+n*f1);
figure(1)
plot (f,abs(z))
xlim([-2*f0 2*f0])
figure(2)
plot(f,abs(z),sidf,sidamp,'o')
xlim([f0-f1*10 f0+f1*10])            % sidebands at the pos frequencies

Fig 1 shows positive and negative frequencies. Most of the time people double the abs(amplitudes) and show positive frequencies only, in which case the sideband calculation does not have the factor of 1/2.

MATLAB: What does the notation ( ‘ ) in the time sample t = (0:dt:0.002-dt) ‘ mean ??and thanks in advance

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.

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