What is the Pink Noise and White noise On your own, research the nature of pink

Question

What is the Pink Noise and White noise

On your own, research the nature of pink noise and how it is different from the uniformly distributed white noise. Use the help documentation links shown below to investigate how a pink noise sequence is generated in MATLAB DSP Systems Toolbox.   

Links you can find the answer:

http://www.mathworks.com/help/dsp/ref/dsp.colorednoise-class.html#bt94_hd-3   

http://www.mathworks.com/help/dsp/ref/dsp.colorednoise-class.html

http://www.mathworks.com/help/dsp/ref/dsp.colorednoise.step.html  

Generate the pink noise sequence. The length of the pink noise sequence should be the same as that of the ECG atrial fibrillation signal. Multiply the noise sequence by a factor that would make it relatively equivalent in amplitude to the white noise sequence. Plot the pink noise sequence as a function of data index.

Extra website:

https://en.wikipedia.org/wiki/Noise_(signal_processing)

Explanation / Answer

Pink noise is a type of signal that contains all of the sound frequencies that fall within the range of a human being’s hearing — from the lowest pitches that a person can hear to the highest tones. A variation of white noise, it is usually created when these audible tones are joined together at the exact same time and density. It is sometimes referred to as 1/f noise or flicker noise.

Distinct from white noise, pink noise emphasizes lower frequencies, and its amplitude drops off at a constant rate for each octave, typically three decibels. With pink signals, lower sound frequencies are usually louder and have more power than higher frequencies.

%How to generate Pink noise in Matlab/Octave

function y = add_awgn_noise(x,SNR_dB)

    %y=awgn_noise(x,SNR) adds AWGN noise vector to signal 'x' to generate a

    %resulting signal vector y of specified SNR in dB

    rng('default');%set the random generator seed to default (for comparison only)

    L=length(x);

    SNR = 10ˆ(SNR_dB/10); %SNR to linear scale

    Esym=sum(abs(x).^2)/(L); %Calculate actual symbol energy

    N0=Esym/SNR; %Find the noise spectral density

    if(isreal(x)),

        noiseSigma = sqrt(N0);%Standard deviation for AWGN Noise when x is real

        n = noiseSigma*randn(1,L);%computed noise

    else

        noiseSigma=sqrt(N0/2);%Standard deviation for AWGN Noise when x is complex

        n = noiseSigma*(randn(1,L)+1i*randn(1,L));%computed noise

    end    

    y = x + n; %received signal    

end

Comparison & Testing

t = 0:.1:10;%time base

x = sawtooth(t); % Create sawtooth signal.

%Method 1: using custom function 'add_awgn_noise

rng('default');%set the random generator seed to default (for comparison only)

%If the seed above is not set, the results may vary from run-run

y_custom = add_awgn_noise(x,SNR_dB); %our custom function

%Method 2:Using in-Built Function (needs comm toolbox)

rng('default');%set the random generator seed to default (for comparison only)

y_inbuilt = awgn(x,SNR_dB,'measured'); % Add white Gaussian noise.

%Plotting results

figure; subplot(1,2,1);

plot(t,x,'b',t,y_custom,'r') % Plot both signals.

legend('signal','signal with noise');

xlabel('timebase');ylabel('y_{custom}');

title('custom add_awgn_noise function')

subplot(1,2,2); plot(t,x,'b',t,y_inbuilt,'r') % Plot both signals.

legend('signal','signal with noise');

xlabel('timebase');ylabel('y_{inbuilt}');

title('Inbuilt awgn function')

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