Coherence and the Cross Spectrum

[@rotehrerikcecb4323]

Everything is so clear as you pinpoint all the remarkable details one should think about, and as you make mathematical steps reveal their simplicity ! I discovered your channel a few days ago, and I've made so much progress in understanding those fields of digital signal processing and machine learning. I'm in academic and teaching too and want to emphasize the very good and effective job done using only hand-made drawings and hand-written text. You reveal that knowledge is always easy to propagate if one wants to put effort in the process. Thank you so much, keep up the so good work, please ! You're a must see channel !

[@feicuitadie]

Barry, really appreciate your work!

[@shijian5846]

What a clear explanation! Really helpful and art-like teaching. Thanks.

[@khaledsalem9617]

thanks for the explanation. I have an a question. Can we calculate the time delay between two signals when they are recorded at different times?

[@jankonig2333]

Wow, nice!!! Thank you very much! Clear explanation.

[@George-ni5ic]

Exceptionally well presented.

[@mayainseoul]

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????

[@iSoulbound]

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

[@llaskin]

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?

[@allsignalprocessing]

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.

[@nishantgaurav3027]

sir can u illustrate cross correlation graphically.I m not able to get numerically.Plese illustrate it graphically using two signal.

[@llaskin]

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?

[@allsignalprocessing]

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.

[@llaskin]

It is what I suspected and I will watch your videos on DFT. Thanks a lot for the explanation, your videos are very helpful!

[@mirimoers]

Thanks for helping !

[@samirelzein1978]

good job!

[@eitanas85]

I think that a concrete examples would have made his video much much better. anyway, great video!

[@taoyang8204]

thx