💥1 概述
文献来源：
摘要:本文研究了具有任意谱斜率的幂律彩色数字噪声信号(序列)的生成。首先，简要介绍了一些噪声特征的背景信息。在此基础上，提出了一种基于白噪声信号的产生、频域变换、频谱处理和逆变换回时域的方法。进行了计算机模拟以确认算法的一致性，包括功率谱密度的估计和自相关性，以及与相应的内置Matlab®函数相比其优异性能的示例。
关键词:彩色噪声，粉色噪声，红色噪声，蓝色噪声，紫色噪声，生成
原文摘要：
📚2 运行结果
部分代码：
% function: x = arbssnoise(N, alpha)
%
% Input:
% N - number of samples to be returned in the noise column vector
% alpha - PSD spectral slope
%
% Output:
% x - column vector of noise samples with unity
% standard deviation and zero mean value
%
% For instance:
% black noise -> alpha < -2, PSD slope < -20 dB/dec;
% red noise -> alpha = -2, PSD slope = -20 dB/dec;
% pink noise -> alpha = -1, PSD slope = -10 dB/dec;
% white noise -> alpha = 0, PSD slope = 0 dB/dec;
% blue noise -> alpha = +1, PSD slope = 10 dB/dec;
% violet noise -> alpha = +2, PSD slope = 20 dB/dec;
function x = arbssnoise(N, alpha)
% input validation
validateattributes(N, {'double'}, ...
{'scalar', 'integer', 'nonnan', 'finite'}, ...
'', 'N', 1)
validateattributes(alpha, {'double'}, ...
{'scalar', 'real', 'nonnan', 'finite'}, ...
'', 'alpha', 2)
% convert from PSD (power specral density) slope
% to ASD (amplitude spectral density) slope
alpha = alpha/2;
% generate AWGN signal
x = randn(1, N);
% calculate the number of unique fft points
NumUniquePts = ceil((N+1)/2);
% take fft of x
X = fft(x);
% fft is symmetric, throw away the second half
X = X(1:NumUniquePts);
% prepare a vector with frequency indexes
n = 1:NumUniquePts;
% manipulate the left half of the spectrum so the spectral
% amplitudes are proportional to the frequency by factor f^alpha
X = X.*(n.^alpha);
% perform ifft
if rem(N, 2) % odd N excludes Nyquist point
% reconstruct the whole spectrum
X = [X conj(X(end:-1:2))];
% take ifft of X
x = real(ifft(X));
else % even N includes Nyquist point
% reconstruct the whole spectrum
X = [X conj(X(end-1:-1:2))];
% take ifft of X
x = real(ifft(X));
🎉3 参考文献
[1] H. Zhivomirov. A Method for Colored Noise Generation. Romanian Journal of Acoustics and Vibration, ISSN: 1584-7284, Vol. XV, No. 1, pp. 14-19, 2018.
