How do you add noise to an FM signal?

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Jared Joselowitz
Jared Joselowitz 2020-9-9
回答： Manuel A. Vázquez López 2021-3-27
This is Frequency modulation where
where
Question:
I have been able to modulate the message signal m(t) and demodulate it suing this code:
fc = 1000;
Ac = 5;
t0 = 0.2;
ts = 0.00000001;
fs = 1/ts;
t=[0:ts:t0];
m = 10*t.*(t>=0 & t<=0.1)+(2-10*t).*(t>0.1 & t<=0.2)+0.*(t>0.2);
u = Ac*modulate(m,fc,fs,'fm'); %% modulate the message signal
y = demod(u,fc,fs,'fm'); %% demodulate the message signal
y = y/(6.275*10^-5); %% scale the demodulated signal
figure(6)
subplot(2,1,1)
plot(t,m(1:length(t)));
title('Original Message signal m(t)')
xlabel('Time (s)')
ylabel('Amplitude')
subplot(2,1,2)
plot(t,y);
title('Demodulated Message Signal')
xlabel('Time (s)')
ylabel('Amplitude')
I now need to add noise to the signal according to the above formula of y(t) = u(t) + n(t)
where n(t) = nc(t).cos(2\pi fc.t) - ns(t).sin(2\pi fc.t)
How do I add this noise to u(t) using rand or randn ?

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回答（2 个）

Hiro Yoshino
Hiro Yoshino 2020-9-9
You can check this up:
https://jp.mathworks.com/matlabcentral/answers/80714-how-generating-band-limited-white-noise-with-matlab
Basically you should follow this:
  1. white noise
  2. apply filter with the cutoffs both ends in the frequency domain
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Jared Joselowitz
Jared Joselowitz 2020-9-10
I have added the noise however, the demodulated signal is indestinguishable from the orignal message signal:
fc = 1000;
Ac = 5;
kf = 25;
t0 = 0.5;
ts = 0.00000001;
fs = 1/ts;
t=[0:ts:t0];
df = 0.45;
nc = 0.2;
ns = 0.2;
m = 10*t.*(t>=0 & t<=0.1)+(2-10*t).*(t>0.1 & t<=0.2)+0.*(t>0.2);
u = modulate(m,fc,fs,'fm');
n = nc*cos(2*pi*fc*t) - ns*sin(2*pi*fc*t);
y = u + n;
dem = demod(y,fc,fs,'fm'); % demodulate the nosey signal
dem = dem/(8.7275*10^-5); % scale the signal
figure(1)
subplot(2,1,1)
plot(t,m(1:length(t)));
title('Original Message signal m(t)')
xlabel('Time (s)')
ylabel('Amplitude')
subplot(2,1,2)
plot(t,dem);
title('Demodulated Noisy Message Signal')
xlabel('Time (s)')
ylabel('Amplitude')

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Manuel A. Vázquez López
Long time but...did you get to solve this? I'm facing a similar problem. I'm adding some Gaussian noise with standard deviation 1e-2, but that has a huge impact on the demodulated signal (and I was assuming FM should be fairly resilient to it).

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