MATLAB: How to insert noise in a signal using matlab

noise

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.

Best Answer

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.)

Related Solutions

MATLAB: Bandpassing of a signal

An equivalent elliptic filter (essentially the same one the bandpass function would design):

Fs = 1000;                                          % Sampling Frequency
Fn = Fs/2;                                          % Nyquist Frequency
Wp = [100 200]/Fn;                                  % Passband Normalised
Ws = [ 90 210]/Fn;                                  % Stopband Normalised
Rp =  1;                                            % Passband Ripple (Irrelevant in Butterworth)
Rs = 50;                                            % Stopband Attenuation
[n,Wp] = ellipord(Wp,Ws,Rp,Rs);                     % Order Calculation
[z,p,k] = ellip(n,Rp,Rs,Wp);                        % Zero-Pole-Gain 
[sos,g] = zp2sos(z,p,k);                            % Second-Order Section For Stability
figure
freqz(sos, 2^16, Fs)                                % Filter Bode Plot
x_filt = filtfilt(sos, g, x);                       % Filter Signal

Here, ‘x’ is the signal vector. To reproduce the plot, create an equivalent signal (this one from the bandpass documentation page):

fs = 1e3;
t = 0:1/fs:1;
x = [2 1 2]*sin(2*pi*[50 150 250]'.*t) + randn(size(t))/10;

then apply my filter design to it.

To create the second plot, divide the fft of ‘x_filt’, by the fft of ‘x’ using element-wise division, then plot as you normally would plot the fft. See fft for details.

MATLAB: Query on DFT plotting

It is plotting only the first half of the fft result ‘x_mags’ from 0 to π radians. This is the usual approach, since ‘x_mags’ is actually symmetrical, with the second half being the complex conjugate of the first half. (There is usuallny no reason to plot both halves, unless you are using fftshift and plotting from

to π in this instance. That is not the situation here.)

Best Answer

Related Solutions

MATLAB: Bandpassing of a signal

MATLAB: Query on DFT plotting

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