# Notes to myself

#### apr 2003

Notes to refresh what's left of my memory (or: "an attempt to postpone the losing battle with entropy").

#### Signal processing:

going from continuous to discrete fourier transform
sin(x)/x
polyphase filterbanks.
gaussian width after convolving 2 gaussians.
Jon Hagen's acf-> spectra memo (.pdf)
rms voltages needed for 2,3,4, and 5 bit sampling.
clipping a sine wave

Computing Trcvr.
Telescope gain
Yfactor, measuring Tscattered for horn on antenna.

pulsarNotes
Beamwidth, near/far field transition
satellite orbits: velocity,angular velocity, period vs radius
sun,moon separation during 21aug17 eclipse

#### Idl use of color

Using idl to process ao spectral line data
• side band harmonics do not always move farther out than at the fundamental. (top)
Suppose you have a tone of  Amplitude A and frequency w and a side band of amplitude B  and frequency (w+delta)
then:
(Aexp(iwt)+Bexp(i(w+delta)*t)2= AAexp(i2wt)+ ABexp(i(2wt +delta)) + BB*exp(i(2w+2delta)t)
If B << A then the AB term will be much larger than the BB term so the +delta signal will be stronger than the 2*delta.

• Gaussian: (top)

• A gaussian centered at x=0 can be  defined as:
y1= 1./sqrt(2*pi)*e-.5*(x/sig)^2)   integral normalized to unity
y2=                          e-(x/sig)^2)    y2(x=0)=1.     y2(x=1)=e-1= .367879
Properties are:
 property y1 y2 maxvalue y(0) y1(0)=.398942 y2(0)=1. y(sig) y1(sig)=.2419707 y2(sig)=.367879 integral -inf to inf 1. sqrt(pi)=1.77245 FWHM=m*sig (see  1*) sig=n*FWHM m=2.35482 n=.424661 m=1.66511 n=.60056118

1*
y1=A0/2=A0*e(-.5*x/sig)^2)
sqrt(2*ln(2))*sig=x(hwhm)
FWHM=2*x =2*sqrt(2*ln(2))
y2=1/2=e(-(x/sig)^2)
sqrt(ln(2))*sig=x(hwhm)
FWHM=2*x= 2*sqrt(ln(2))*sig

• sin(x)/x  (top)

• y=sin(x)/x . If x is defined in units of the first null, then use sin(pi*x)/(pi*x)
 property maxvalue : y(0) 1. minvalue  :y y=-.2172336, x=4.4934100.. zero crossings pi*n n=1.. peaks,min when x=tan(x) (more info) for large x :close to x=(2n+1)pi/2 x when y=.5 x=1.8954950 integral between 1st  nulls (-pi,pi) integral: 9.8696191

#### rms voltages needed for 2,3,4, and 5 bit sampling.  (top)

The optimum voltage levels for 2, 3, , and 5 bit sampling were computed using the threshold levels from fred schwab. To compute the rmsVolts I just took PktoPkVolts/Nlevels * sigmaLevels. This ignores the problem of whether or not the levels are centered on 0 volts or not.

 Nbits level threhsold (in sigmas) Sigma (1./level) (in levels) rms (Volts) assuming 2V PkToPk A/D rms (Volts) Assuming 5V PkToPk A/D (ri) 2 .99568 1.004 0.502 1.255 3 .58601 1.706 0.427 1.067 4 .33520 2.983 0.373 0.932 5 .18814 5.315 0.332 0.830

#### Compute Trcvr.  (top)

The receiver temperature is computed using a hot and cold load at the input. let:
• T1 and T2 be the temperatures of these loads.
• gamma is the voltage reflection at the input to the horn. let G2=(1-gamma^2). It will be the fraction of the input power that gets into the device
• alpha is the loss in the omt, Tomt is the temperature of the omt. (1-alpha) of the entering temp will be passed through. (1-alpha)*Tomt will be contributed by the omt temp.
• Tamp is the amplifier temperature. Trcv is normally Tamp +  alpha*Tomt.
`Y=Pwr2/Pwr1 y=(Tamp + alpha*Tomt + (1-gamma^2)(1-alfa)T2)/(Tamp + alpha*Tomt + (1-gamma^2)(1-alpha)T1)`
Solving for Tamp gives:
`Tamp(1-Y)=Y(alpha*Tomt + (1-alpha)(1-gamma^2)*T1) - (alpha*Tomt + (1-alpha)(1-gamma^2)T2)`
`Tamp= (1-alpha)(1-gamma^2)*(T2-Y*T1)/(Y-1) - alpha*Tomt`
If you assume that alpha,gamma are equal to zero, then you will get a Tamp that is higher than it really is.

#### Telescope gain  (top)

Some formulas
• Ae= effective area (aperture). (PowerExtracted/IncidentFlux)
• nA=aperture efficiency ( Ae/Ag) Ag=geometric aperture)
• D=Gmax=4piAe/(lamda^2) or
• Ae*bmSa = lamda^2 (bmSa=beam solid angle)

Units:

k - boltzman's constant
K - deg Kelvin
Jy - Jansky
m - meters
w = watts
J   - Joules
Hz- hertz
Ae - effective area of telescope
G  - gain
T   - Tsys
 item value notes k: Boltsmans' Constant 1.38e-23 Joule/degK -228.6 db/degK -198.6 dbm/degK convert TempK to energy Joules Jy: Jansky 1e-26 W/(m^2*Hz) -260  db/(m^2*Hz) -230  dbm/(m^2*Hz) flux density per hz k/Jy:boltzmans constant/Jy        (J/K)/(w/(m^2*Hz) 1380  (m^2/K) for 1 Jy dual pol? 2760 (m^2/K)  for 1 Jy single pol? A telescope with Ae=2760 m^2 give: Ae/2760 = 1K for a 1 Jy source Gain 1K/Jy = 2760m^2 G = K/Jy = Ae/2760. G/T = (Ae/T)/2760. SEFD=T/G = (T/Ae) * 2760. plot sefd vs T/Ae  (.ps) (.pdf) nrao Brightnes and Flux density
• 1 K/Jy is 2760 m^2
• for a uniformilly illuminated circular appeture: hpbw=1.02*lambda/D
• if plane wave with energy power density S hit telescope. The telescope extracts Pe energy then the effective area of the telescope is Ae=Pe/S
• The appeture efficiency is Na=Ae/Ag  where Ag is the geometric area.
• Gmax=4*pi*Ae/lambda^2
• Ae*OmegaA=lambda^2 where OmegaA is the beam solid angle (integrated over 4pi steradian).
• OmegaMb is the main beam solid angle. Defined to be the solid angle that has the same area as the mainbeam down to the first nulls.

# Pulsars

• dm smearing across a band
• tmSmMillisecs= (202/cfrMhz)^3 * dm *BwMhz
• optimum channel width for incoherent processing
• 1/channelwidth  = dmsmearing across the channel..
• or
• 1./(bw/nchan) = dmSmearingbw/nchan
• nchan/dmSmearingBw = bw/nchan
• nchan= sqrt(bw*dmSmearingBw)  optimum.. or
• nchan=sqrt(bwMHz^2 * (202/cfrMhz)^3 * dm * 1e3)

# Satellite orbits

• Page 1: orbits vs radius from center of earth
• top: velocity km/sec
• 2nd: velocity km/hour
• 3rd: obital angular velocity
• 4th orbital period in hours
• Page 2: orbits versus distance above the earth
• Page 3: blowup showing 0.. 1000 km above the earth's surface.
• The dashed red lines shows the geostationary orbit.
• Page 4: How long a satellite is above the observers horizon (assuming sea level, min elevation=0)
• Page 5: How fast does a telescope need to move to track satellites at various heights..
• red lines show the 12meter limit (50 km?) and the 305 m limit (6000 km).
• The lines are the max velocities.. you probably can't track continually at this speed (you always need a little extra if you ever need to catch up..).
processing: x101/131107/satorbit.pro

# 170821 sun moon separation as see from AO

I plotted up the sun,moon separation for the 21aug17 eclipse (as seen from arecibo observatory).
I used the jpl horizons ephemerides to compute the separation.

• the moon, sun edges will start to intersect at 14:18 ast
• the minimum distance (maximum for eclipse) will occur at 15:34:00.3 ast
• the minimum separation (of their centers) will be .099 degrees (about 6 arc minutes).
• the moon , sun will finish their overlap at 16:40
processing: x101/170821/eclipse.pro

# svn

## repository structure

• How directories are used:
• trunk
• main developement goes on here
• branches
• Different versions stores with possible updates needed to fix a version
• tags:
• snapshots of a particular version. It is frozen. Might be easier to role back

• /share/megs/phil/svnrepos  : the repository
• Cima
• branches
• mocksp
• Software
• tags
• V3.0.10    (normal)
• Software
• V3.1.03     (smart)
• Software
• trunk
• Software
• idl -  holds  phil's idl code
• branches
• tags
• trunk
• idl directories under /pkg/rsi/local/libao/phil
• pdev - the datataking system for pdev. excludes jeff's code
• branches
• tags
• rev-1026/  before parallactic angle changes 16feb09
• rev-879/    before psrfits changes.
• trunk
• aosoft/
• linux.sh
• linuxfiles/
• pdev/
• vw - vxWorks datataking code from /home/phil/vw/
• branches
• tags
• trunk
• directory under /home/phil/vw/
• vwTcl - tcl procedures for vxWorks. from /home/online/vw/Tcl
• branches
• tags
• trunk
• code from /home/online/vw/Tcl

## svn commands

• list contents of repository:
• svn list file:///share/megs/phil/svnrepos
• copy a new set of files into the repository
• svn import

## svn notes CIMA

• Locations:
• file:///share/megs/phil/svnrepos/Cima   .. repository
• Online cima versions:
• /home/cima/Software/XX   XX= Mocksp, Svnwork
• Working directories
• /home/cima/svn/Cima/XX     XX = svnwork,mocksp, etc..
• svn list file:///share/megs/phil/svnrepos/Cima
• checkout to a working directory
• cd /home/cima/svn/Cima/ ; mkdir mocksp
• svn -r revision checkout file:///share/megs/phil/svnrepos/Cima/trunk  /home/cima/svn/Cima/mocksp
• Make Svnwork a new cima version release (eg. Mocksp)
• make sure svn repository uptodate for svn/Cima/svnwork svn -u status
• record svn version number
• cd /home/cima/svn/Cima/svnwork
• make install
• moves most recent updates to Svnwork
• does a cmake install aon Frontend,Exectuive, tcl_utilities, then copies the version files back to Cima/svnwork/Software.
• add /home/cima/bin to front of path variable (to find cmake)
• Copy online version Svnwork to new version
• cima_copy Svnwork Mocksp