Robert Kern wrote: > Travis E. Oliphant wrote: > >> Robert Kern wrote: >> >>> Neal Becker wrote: >>> >>> >>>> I noticed that if I generate complex rv i.i.d. with var=1, that numpy says: >>>> >>>> var (<real part>) -> (close to 1.0) >>>> var (<imag part>) -> (close to 1.0) >>>> >>>> but >>>> >>>> var (complex array) -> (close to complex 0) >>>> >>>> Is that not a strange definition? >>>> >>>> >>> 2. Take a slightly less naive formula for the variance which seems to show >>> up in >>> some texts: >>> >>> mean(absolute(z - mean(z)) ** 2) >>> >>> This estimates the single parameter of a circular Gaussian over RR^2 >>> (interpreted as CC). It is also the trace of the covariance matrix above. >>> >>> >> I tend to favor this interpretation because it is used quite heavily in >> signal processing applications where "circular" Gaussian random >> variables show up quite a bit --- so much so, in fact, that most EE >> folks would expect this as the output and you would have to explain to >> them why there may be other choices that make sense. >> >> So, #2 is kind of a nod to the signal-processing community (especially >> the communication section). >> > > <sigh> Fair enough. I relent. You implement it; I'll document the > correct^Wcov() > alternative. :-) > > Not that I find the argument pertinent most of the time, but if there is no clear argument in favor of one formula, would following matlab conventions be ok ?
To me, the definition 2 makes more sense, as a perticular case of the correlation between two different complex random variables: \mathbb{E}[X \bar{Y}], such as it keeps the nice properties of scalar product. cheers, David _______________________________________________ Numpy-discussion mailing list Numpy-discussion@scipy.org http://projects.scipy.org/mailman/listinfo/numpy-discussion