remind them of correl/convol thm's;

the correlation of the two in one domain becomes the product of the two
in the other domain.

thus

A corr B in time domain gives FT(A) times FT(B) in other domain.

this also leads to the identity

FT (ACF (V)) = FT(V) * comp conj FT(V) = pwr spectrum 

illus with the horn data. 

gv acf_acrplot.ps

talking points: 

1. top panel is power spectrum: red and black similar, but not quite
	identical. 

2. panel 2 shows that for the spike, a bif diff--P(f) from ACF goes
negatave! 

3. P(f) comes from FT(ACF). ACF is in panel 3, 4. it looks like mainly
zeros for tau > 2 microsec, but those small numbers repeat thoussands of
times and have most of the info!

4. To have a reasonably high ACF, you need small tau. in particular, the
first zero is at about 0.3 microsec. The bandwidth is, say, 2 MHz
or 4 MHz. (1/B) = (1/4MHz) = 0.215 microsc. 

FOR THE INTERFEROMETER, B=30 MHz, so first zero is at 3.3e-8 sec or 33
nsec. during this time, length traveled by light is ct = 3e8 * 3.3e-8 =
10 meters, about half our baseline. at west horizon, east telescope is
delayed from west by B and at east, west from east by B, a total change
of 2B, or about 35 meters, equiv to a change in time delay of (35/3e8) =
1e-7 sec, 3 times longer than tau at first zero. 

now, explore monochromatic waves. 

gv xv_vs_fx_1.ps

the two P(f)s (black/red) differ. but if time interval wene to infty,
there would be no leakate power and they would be identical.

all is not lost for ACF method; do Hanning smoothing. makes the two
estimates almost identical (green).

gv xv_vs_fx_2.ps

shows what we convolvew with in freq space to get rid of sinx/x. makes
sense from an intuuitive stanedpoint.

now use corrl thm: a convol in freq space is a multiplication in time of
the two FTs in time space. The FT of the hanning spoke is 0.5 + 0.5
cos() (middle panel). 

this is called 'tapereing'. you trae rresolution for
sidelobes. application to telescopes...to reduce spatial sidelobes.

Remark on the use of 'correlators' in radio spectroscopy.