Coherence and the Cross Spectrum
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- Опубликовано: 12 сен 2024
- Coherence and the cross spectrum describe the relationship between two random signals in the frequency domain based on their second order statistics (auto and cross correlation). The cross spectrum is the DTFT of the cross correlation between the two signals and the magnitude squared coherence is the magnitude squared of the cross spectrum normalized to by the power spectrum of the signals. The magnitude squared coherence is unity for signals that are related through a linear time invariant system.
Barry, really appreciate your work!
What a clear explanation! Really helpful and art-like teaching. Thanks.
Wow, nice!!! Thank you very much! Clear explanation.
Exceptionally well presented.
I think that a concrete examples would have made his video much much better.
anyway, great video!
Hi. I hope you can still read this.. Quick question: If I have two signals (acceleration g), how can I put those input in the cross correlation equation? Is it possible to calculate it numerically? Thanks
I've been trying to get a good intuition about how to interpret coherence between two time series in a particular frequency band and I'm not entirely confident I understand it well. Could you give some intuition?
Does it mean that if the time series are coherent in, say, the 8-13 Hz band, they are necessarily phase locked in that band? Or does it mean something more (or something less) than that?
Coherence tells you the degree of phase locking if the signal amplitudes are not varying. So high coherence would imply a high degree of phase locking in that band.
It is a bit more complicated if the amplitudes of the signals are also varying randomly, because coherence also indicates the degree to which the amplitudes are locked. For example, if the signals were perfectly phase locked by the amplitudes were independent, then the coherence would be zero.
Though your explanation is clear, i am confused on how to find cross spectrum for 2 time series and these 2 signals are EEG signals. Can you explain me how to do it and is cross spectrum and cross spectral density is the same????
sir can u illustrate cross correlation graphically.I m not able to get numerically.Plese illustrate it graphically using two signal.
Thanks for helping !
good job!
Can I use DFT instead of DTFT in calculating spectra and cross-spectra? Or can I only do that if I assume the signal is periodic?
Yes. Actually the DFT is the only way to numerically compute spectra and cross-spectra. The DTFT is an analytical tool that assumes infinite duration and continuous-valued frequency. When you approximate the DTFT for numerical computation you have to truncate the duration and sample in frequency, which then becomes a DFT. My video "Using the DFT to Approximate the FT" explains this process.
Once you use the DFT (your only option) there is an implied notion of periodicity in time, but this can be managed by zero padding in time, which is equivalent to evaluating it at a dense set of frequencies.
It is what I suspected and I will watch your videos on DFT. Thanks a lot for the explanation, your videos are very helpful!
thx