How to mark 95% confidence interval with single bar line - example image
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Hello
I'm using the pwelch method of power spectral density estimate, and would like to indicate the confidence interval like as one single bar - just like in the example image attached. At the moment I just plot the pxxc confidence interval array obtained when calling it in the pwelch function, and its looks very confusing (a lot of noise!). Would much prefer to have something like in the image shown...
Thanks!
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Paolo
2014-8-21
Hi, I've seen the answer about single bar to represent confidence interval using pwelch. If I well understood the ratio U/L is constant, therefore the logarithm of the confidence interval has constant difference and depends only on M (the range of frequencies). So in theory, whatever power spectra I obtain, the error will be always the same if I use the same M. For instance I could have several spectra in a single plot with a single errorbar. However, if I try the suggested method I obtain different U and L values depending on the data I provide. Am I doing something wrong? Could you help me? Thanks in advance
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Wayne King
2014-7-19
Do you have the Statistics Toolbox? If so, you can use errorbar()
For example
Fs = 1000;
t = 0:1/Fs:.296;
x = cos(2*pi*t*200)+randn(size(t));
[Pxx,F,Pxxc] = pwelch(x,[],[],[],Fs,'ConfidenceLevel',0.95);
L = mean(10*log10(Pxx)-10*log10(Pxxc(:,1)));
U = mean(10*log10(Pxxc(:,2))-10*log10(Pxx));
plot(F,10*log10(Pxx)); hold on;
errorbar(350,-22,L,U,'ko');
xlabel('Hz'); ylabel('dB');
Note it is important that you plot the PSD estimate in dB because the logarithm is variance-stabilizing for PSD estimate (otherwise the width of the confidence interval is not independent of frequency).
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