How to insert noise in a signal using matlab?

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Nur Fauzira Saidin
Nur Fauzira Saidin 2015-11-5
评论： Star Strider 2015-11-5
Hi. I want to create a signal with noise. I found this coding but I don't know how it works. Can somebody explain this to me?
x= cos(2*pi*12*[0:0.001:1.23]);
x(end) = [];
[b a] = butter(2,[0.6 0.7],'bandpass');
filtered_noise = filter(b,a,randn(1, length(x)*2));
x = (x + 0.5*filtered_noise(500:500+length(x)-1))/length(x)*2;
This is the result when I plot the x.

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Star Strider
Star Strider 2015-11-5
It creates a signal in ‘x’, then creates band-limited noise by bandpass-filtering a Gaussian random vector (created by the randn call), the same length as ‘x’, and stores it in the ‘filtered_noise’ variable. It then adds that to the original ‘x’ and scales it to create the final value of ‘x’. (There is a bit more involved in the code than I described, but that is the essence of it.)
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Nur Fauzira Saidin
Nur Fauzira Saidin 2015-11-5
The length of 'x' is 1230, so the final amplitude is 1/(1230/2) = 1.63x10-3. Okay I understand it now. Thanks! Now if you don't mind, can you help me with the next step? I want to plot the frequency spectrum of signal 'x'.
%plot magnitude spectrum of the signal
X_mags = abs(fft(x));
figure,plot(X_mags);
xlabel('DFT Bins');
ylabel('Magnitude');
Then, this code is to plot the first half of DFT. I don't quite understand this part. Can you explain this to me?
%plot first half of DFT (normalised frequency)
num_bins = length(X_mags);
figure,plot([0:1/(num_bins/2 -1):1], X_mags(1:num_bins/2));
xlabel('Normalised frequency (\pi rads/sample)');
ylabel('Magnitude');
Star Strider
Star Strider 2015-11-5
That appears to be correct.
If you want the frequency in Hz (again assuming the time unit is seconds), multiply the normalised frequency by Fn, or 500 Hz.

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