AST460: Assignment 6 
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(Oct 28 2016)

Process your observations following these instructions 
(a brief outline is also provided in Section 5 of the "Project Intro" document):

1. Using class notes, read one of your data files in IDL and place data in a 2-dimensional 
array representing a stack of spectra (each row of the array will be a single
HI spectrum).

2. Using the information provided in your data file, build a frequency array
for your observations. Plot a single HI spectrum vs frequency.
Please note that your y-axis shows Antenna Temperature in units of Kelvin as the noise calibration
(noisecal) applied automatically the conversion from arbitrary telescope units to K.
Please label your axes.

3. Average all HI spectra after the cal_on and cal_off spectra to produce a single HI spectrum.
Plot this average HI spectrum vs frequency. Please label your axes.

4. Deriving the Filter shape function:

Identify your cal_on and cal_off spectra in your data file.

Using cal_on and cal_off scans calculate the spectral shape or gain function 
(use the equation provided in class notes but smooth or boxcar average this spectrum using a 5-bin window).
Plot this spectral shape function vs frequency. Note that the noise diode has a temperature of 356 K.
Over most of the frequency range shape function should have a value close to 1.
Please note and let me know if this is not the case.

5.
Frequency to Velocity conversion: 
Use the Doppler equation to convert from Frequency to the Topocentric Radial Velocity. 
To convert from Topocentric to LSR Velocity you will need to ADD a correction factor
to your velocity array. The correction factor depends on the observing direction, 
as well as the time of observations.
I will calculate and provide the correction factor.

Plot the average HI spectrum vs Topocentric Radial Velocity. Please label your axes.

6. Produce the average HI spectrum corrected for the spectral gain and plot this 
spectrum as a function of the LSR velocity.

As you can see from class notes, this shape-corrected HI spectrum should be flat at velocities
without significant HI signal, but it is still sitting on a pedestal provided by 
the system temperature. To remove this constant value, find a signal-free range of velocities 
and estimate the mean value of spectral data points. 
Remove this constant value from your shape-corrected HI spectrum to produce the final HI spectrum.
Plot this resultant spectrum as a function of the LSR velocity. 

IMPORTANT:
Please focus on one data file first to make sure all steps are working well.
But write your processing script/procedure by having in mind that you will
have several data files.