mocheck
Newbie level 2
Dear all,
Suppose I have two signal time series x(t) and y(t) recorded simultaneously and sampled with the same sampling rate.
If I understand this correctly, the cross spectrum can be estimated by Fourier-transforming the cross-correlation function, which would be
Sxy(f) = F { E{[x(t)- µx][y(t+τ)-µy]} }
and the coherency between x(t) and y(t) in the frequency domain can be calculated by normalizing the cross spectrum by the spectrum of x(t) and y(t),
Cxy(f) = Sxy(f)/sqrt( Sxx(f)*Syy(f) ), which is a function of frequency
According to several papers I am reading which deal with neuronal electrical signal processing, the Cxy(f) is also a measure of the synchrony/phase relationship between x(t) and y(t) at a particular frequency f, where Cxy(f) = 1 refers to constant phase relationship while a value of 0 indicates the absence of any phase relationship.
My questions are as follows:
1 To what I know, Cxy is calculated on the basis of cross spectrum and auto spectrum, which do not contain any phase info of the signal but only the information how power distribution along the frequency domain. So what is the rationale of measuring phase relationship between these two signals within a given frequency band using sth that does not contain any phase info of the signal sequence?
2 In terms of determining phase relationship, wouldn't it be much easier if we simply take the arctan of the Im/Real of the FFT coefficient and calculate their difference at a give frequency f?
Sorry about the amatuerity of my questions but these quetions have been bugging me for a week and I would really appreciate some helpful answers
Many thanks and Best regards,
Ce
Suppose I have two signal time series x(t) and y(t) recorded simultaneously and sampled with the same sampling rate.
If I understand this correctly, the cross spectrum can be estimated by Fourier-transforming the cross-correlation function, which would be
Sxy(f) = F { E{[x(t)- µx][y(t+τ)-µy]} }
and the coherency between x(t) and y(t) in the frequency domain can be calculated by normalizing the cross spectrum by the spectrum of x(t) and y(t),
Cxy(f) = Sxy(f)/sqrt( Sxx(f)*Syy(f) ), which is a function of frequency
According to several papers I am reading which deal with neuronal electrical signal processing, the Cxy(f) is also a measure of the synchrony/phase relationship between x(t) and y(t) at a particular frequency f, where Cxy(f) = 1 refers to constant phase relationship while a value of 0 indicates the absence of any phase relationship.
My questions are as follows:
1 To what I know, Cxy is calculated on the basis of cross spectrum and auto spectrum, which do not contain any phase info of the signal but only the information how power distribution along the frequency domain. So what is the rationale of measuring phase relationship between these two signals within a given frequency band using sth that does not contain any phase info of the signal sequence?
2 In terms of determining phase relationship, wouldn't it be much easier if we simply take the arctan of the Im/Real of the FFT coefficient and calculate their difference at a give frequency f?
Sorry about the amatuerity of my questions but these quetions have been bugging me for a week and I would really appreciate some helpful answers
Many thanks and Best regards,
Ce
