Generate a time series from power spectral density

30 次查看（过去 30 天）
Uwais
Uwais 2024-4-24
评论： Star Strider 2024-4-25
I have a force PSD of 2X2X63 acting at 2 points of 63 frequencies defined. For each frequency, there is a 2x2 matrix representing the auto and cross variances of the force. I want to construct a time signal of 2xN size where N is the size of the time signal. How do I do it?
  4 个评论
显示 2更早的评论
Star Strider
Star Strider 2024-4-24
It is not possible to invert a power spectral density signal. First, the units are in dB/Hz, and second, all the phase information is missing.
Uwais
Uwais 2024-4-24
I see. How about I add a random phase? I dont mind if i dont recover the true time signal.

请先登录，再进行评论。

请先登录，再回答此问题。

采纳的回答

Star Strider
Star Strider 2024-4-24
编辑：Star Strider 2024-4-25
Ran in:
In that event, just create a sine curve of the appropriate frequency or frequencies as determined by the PSD result. This will be a ‘synthesis’ rather than a true inversion, however it is likely as close as you can get with only the PSD and frequency vectors.
Illustrating that —
psd_freq = 0:500;
gp = @(x,d) exp(-(x-d).^2/200);
psd_mag = sum(cell2mat(arrayfun(@(d)gp(psd_freq,d), [10 50 120 250 450], 'Unif',0).')) + 0.01;
figure
plot(psd_freq, psd_mag)
grid
title('Original PSD')
figure
plot(psd_freq, mag2db(psd_mag))
grid
title('Original PSD (dB)')
Fs = max(psd_freq)*2; % Calculated Sampling Frequency (Hz)
L = 5.25; % Length Of Signal (s)
t = linspace(0, Fs*L, Fs*L+1)/Fs; % Time Vector
s = psd_mag(:).*sin(2*pi*t.*psd_freq(:)); % Synthesized Signal Matrix
s = sum(s); % Create One Vector, Add Noise
figure
plot(t, s)
grid
xlim([min(t) max(t)])
xlabel('Time')
ylabel('Amplitude')
figure
pwelch(s,[],[],[],Fs)
Calculatng the PSD of the synthesized signal is not a perfect reproduction of the original PSD, however is reasonably close to it. That implies that the reconstructed time-domain signal is probably representative of the original time-domain signal that created the original PSD. It is not possible to determine how closely the reconstructed time-domain signal reproduces the original time-domain signal without having the original to compare it with.
I encourage you to experiment with this idea.
EDIT — (25 Apr 2024 at 06:10)
Simplified code, expanded discussion.
.
  3 个评论
显示 1更早的评论

请先登录，再进行评论。

更多回答（0 个）

类别

在 Help Center 和 File Exchange 中查找有关 Parametric Spectral Estimation 的更多信息

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by