生成噪声包括:

1)粉红色(闪烁)噪声-功率谱密度斜率-3 dB/oct。， - 10db /dec

2)红色(布朗)噪声-功率谱密度斜率-6 dB/oct。， - 20db /dec

3)蓝色噪声-功率谱密度斜率+3 dB/oct。， + 10db /dec

4)紫色(紫色)噪声-功率谱密度斜率+ 6db /oct。， +20 dB/dec

clear, clc, close all

% signal parameters
fs = 44100;         % sampling frequency, Hz
T = 60;             % signal duration, s
N = round(fs*T);    % number of samples

% noise generation
x = rednoise(1, N); % red noise, PSD falls off by -20 dB/dec

% calculate the noise PSD
winlen = 2*fs;
window = hanning(winlen, 'periodic');
noverlap = winlen/2;
nfft = winlen;

[Pxx, f] = pwelch(x, window, noverlap, nfft, fs, 'onesided');
PxxdB = 10*log10(Pxx);

% plot the noise PSD
figure(1)
semilogx(f, PxxdB, 'r', 'LineWidth', 1.5)
grid on
xlim([1 max(f)])
set(gca, 'FontName', 'Times New Roman', 'FontSize', 14)
xlabel('Frequency, Hz')
ylabel('Magnitude, dBV^{2}/Hz')
title('Power Spectral Density of the Noise Signal')

clear, clc, close all

% signal parameters
fs = 44100;         % sampling frequency, Hz
T = 0.1;            % signal duration, s
N = round(fs*T);    % number of samples
t = (0:N-1)/fs;     % time vector

% signal generation
s = 10*sin(2*pi*1000*t + pi/6);

% noise generation
SNR = 20;                       % define SNR in dB
Ps = 10*log10(std(s).^2);       % signal power, dBV^2
Pn = Ps - SNR;                  % noise power, dBV^2
Pn = 10^(Pn/10);                % noise power, V^2
sigma = sqrt(Pn);               % noise RMS, V

n = sigma*pinknoise(1, N);      % pink noise generation
x = s + n;                      % signal + noise mixture

% plot the signal
figure(1)
plot(t, x, 'r', 'LineWidth', 1.5)
grid on
xlim([0 max(t)])
set(gca, 'FontName', 'Times New Roman', 'FontSize', 14)
xlabel('Time, s')
ylabel('Amplitude')
title('Sine wave signal + Pink noise in the time domain')

% check the SNR
commandwindow
disp(['The target SNR is ' num2str(SNR) ' dB.' newline ...
      'The actual SNR is ' num2str(snr(x, n)) ' dB.'])

clear, clc, close all

% signal parameters
fs = 44100;     % sampling frequency, Hz         
m = 256;        % number of the rows of the noise matrix
n = 256;        % number of the columns of the noise matrix

% noise generation
xred = rednoise(m, n); 
xpink = pinknoise(m, n); 
xblue = bluenoise(m, n); 
xviolet = violetnoise(m, n); 

% visual presentation
figure(1)
colormap gray
subplot(2, 2, 1)
imagesc(xred)
title('Red noise')
subplot(2, 2, 2)
imagesc(xpink)
title('Pink noise')
subplot(2, 2, 3)
imagesc(xblue)
title('Blue noise')
subplot(2, 2, 4)
imagesc(xviolet)
title('Violet noise')

代码由知乎学术咨询获得：
https://www.zhihu.com/consult/people/792359672131756032?isMe=1

工学博士，担任《Mechanical System and Signal Processing》《中国电机工程学报》《控制与决策》等期刊审稿专家，擅长领域：现代信号处理，机器学习，深度学习，数字孪生，时间序列分析，设备缺陷检测、设备异常检测、设备智能故障诊断与健康管理PHM等。