Phase Noise - Kasdin Algorithm

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Tiago Magalhaes
Tiago Magalhaes 2017-2-2
评论： Tiago Magalhaes 2017-2-20
Hi everyone I'm currently working on phase noise 1/f^alpha. Searching for some code, I didn't found a clear example of implementation. So, I've decided to create my own based on Kasdin. Follow my code:
function [X] = PHkasdin(npts, Qd, alfa)
% npts = number of points % Qd = phase noise variance % alfa = kind of phase noise
nn = 2*npts;
ha = alfa/2;
Qd = sqrt(Qd);
hfa = zeros(nn,1);
wfa = zeros(nn,1);
X = zeros(npts,1);
hfa(1) = 1;
wfa = Qd.*randn(size(wfa));
for i = 2: npts %gera os coeficientes hk
hfa(i) = hfa(i-1)*( (ha + (i-2))/(i-1) );
% wfa(i) = Qd*randn();
end
HFA = fft(hfa,nn);
WFA = fft(wfa,nn);
WFA(1) = WFA(1)*HFA(1);
WFA(2) = WFA(2)*HFA(2);
for i = 3: 2: nn
wr = WFA(i);
wi = WFA(i+1);
WFA(i) = wr*HFA(i) - wi*HFA(i+1);
WFA(i+1) = wr*HFA(i+1) + wi*HFA(i);
end
wfa = (ifft(WFA,npts));
for i = 1: npts
X(i) = X(i) + wfa(i)/npts;
end
end
In order to get the graph, I wrote the following code:
clear, clc
% signal parameters Fs = 1e6; % sampling frequency, T = 5; % signal duration, s N = round(Fs*T); % number of samples
alfa = 3; % sigma3 = 2.48e-8; sigma3 = 1.26e-4; % just a variance
% noise generation x3 = PHkasdin(N, sigma3 , alfa);
% calculate the PSD winlen = max(size(x3)); na = 8; window = hanning(floor(winlen/na)); % winlen = Fs/2; % window = hanning(winlen, 'periodic');
[Pxx, f] = pwelch((x3), window, 0, [], Fs, 'twosided'); PxxdB = 10*log10(Pxx);
% plot the PSD figure(1) semilogx(f, PxxdB, 'r', 'LineWidth', 2) grid on hold on;
The resulting graph doesn't have a -30dB/decade slope, in fact have a -20dB/decade.
Could someone help me on this?
Thank you
  2 个评论
Mitsuo Sakamoto
Mitsuo Sakamoto 2017-2-5
Does the Kasdin's algorithm support alfa > 2?
Tiago Magalhaes
Tiago Magalhaes 2017-2-20
Yes, it works for any alfa integer.

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