Craig Markwardt wrote:
> "Thomas Smid" <[email protected]> writes:
> > The sign of the differences between A and B is irrelevant for the
> > angular power spectrum (or do you see any negative values there?). The
> > power spectra are obtained by means of a 'quadratic estimator' i.e. the
> > sign of T1-T2 doesn't matter (see
> > http://lambda.gsfc.nasa.gov/product/map/dr1/ang_power_spec.cfm ). The
> > power spectrum thus reflects directly the standard deviation
> > sqrt(2)*sigma.
> No. You are confusing the *observable*, which is the time series that
> measures the intensity difference between two WMAP receiver feeds, and
> the *derived products* (the angular power spectra and cross
> correlation functions).
> The WMAP observable quite obviously is a signed value, since it
> involves differencing two positive quantities. It is this difference
> that is inherent to the WMAP hardware. The differences are also the
> values used by Page et al (2003; see description of analysis therein).
> Thus your original claims are erroneous. The "standard deviation" is
> *not* the observable, and they contain no hidden bias.
We are discussing here only a 'derived product' i.e. the angular power
spectra. This is cleary independent of the sign of T1-T2 but depends
only on the absolute value which in turn is given by the standard
deviation of the signal as argued above.
> As for the derived products (cross correlations and/or angular power
> spectra), the beam profiles of all the feeds and their cross
> correlations are of course handled in the analysis. I already
> referred to Hinshaw, et al., (2003, ApJS, 148, 135) which describes
> this process.
This paper is not relevant for the details of the beam profiles. You
have to look at L. Page et al, 2003, ApJS, 148, 39 (from which I took
the Fig. 4 on my page http://www.physicsmyths.org.uk/wmap.htm ). It is
clear from this that these beam profiles are for a single telescope (as
they have been obtained by the transit of an individual point source
(Jupiter)), but following my argument from above, they are not
appropriate for differences of identical noisy signals.