                    **********
                    *   TS   *
                    **********

enables you to view and analyze variable star data.



(c) Copyright 1996 by the American Association of Variable
      Star Observers (AAVSO); all rights reserved.



The program TS, and its documentation, are the exclusive
property of the American Association of Variable Star
Observers (AAVSO).  No part of the program, or the
documentation, may be reproduced, distributed, copied,
stored in an information retrieval system, or otherwise
communicated, without the express written permission of
the director of the AAVSO.


            *************************
            *      INSTALLING  TS   *
            *************************


TS is very easy to use on your PC.  It should run on any
IBM PC or PC clone, running DOS 3.1 or higher, with an EGA,
VGA or SVGA display.  There are two ways to "install" it.
One way is simply to copy the two files TS.EXE and TXYZ.TXT
into the directory in which you intend to work.  Then you
can, within that directory, type "TS" to start the program.
If you want to be able to run TS from any directory,
at any time, then do the following:

    1.  Create a directory named AAVSOPRG on your C: drive
        (if one already exists, that's OK).  Then copy the
        files TS.EXE and TXYZ.TXT into that directory.

    2.  Include the directory C:\AAVSOPRG in the PATH statement
        of your AUTOEXEC.BAT file.


            *************************
            *      STARTING-UP TS   *
            *************************


Issue the command "TS" in the directory you're using.  A brief
copyright statement appears.  

CHOOSING HOW TO MOVE

   USING THE MOUSE

     The mouse can be used to make it easier to operate TS:
     
     *  Whenever TS asks you a question, you can click the left
        mouse button instead of pushing <ENTER> on the keyboard.

     *  If TS asks you a yes-or-no question, you can toggle between
        <Y> and <N> by clicking the right mouse button.  

     *  When you want to choose a function from the selection menu,
        you can either press the appropriate function key, or
        place the cursor on top of the function and click the
        mouse's left button.

   USING THE KEYBOARD

      If you do not have a mouse, you can move the cursor
      with the keyboard.

       a  Moving around the screen
         The following keys control movement:
   
            arrow keys                  slow 
            <Control>+<Left Arrow>      fast LEFT
            <Control>+<Right Arrow>     fast RIGHT
            <Page Up>                   fast UP
            <Page Down>                 fast DOWN
            <Home>                      extreme LEFT
            <End>                       extreme RIGHT

       b  Choosing options:

       *    To simulate a mouse click, push <ENTER>.

       *    To select an option , press the appropriate function key.
            For example, to refresh the screen, press the <F9> key.


            *************************
            *       LOADING DATA    *
            *************************


LOADING AT START-UP

   CHOOSING A DATA FILE

      TS asks from which file it should load data.

                    Data File =

      If your file is in another directory or another drive,
      enter the file's full path\name.  If your file is in the
      same directory you're working in, enter the file's name.

   NAMING THE LOG FILE

      Suppose your data file was called MYFILE.DAT.  Then
      TS asks you

        Log File = MYFILE.TS

      TS is asking you to name the log file, which will save
      information during your analysis.  As you perform certain
      analyses of the data, many of the results should be saved
      for later examination.  These results are recorded in the
      log file.  If you want to use the default name, push <ENTER>.
      If you want to use a different name, type it in.  You can
      use this log file every time you run TS because the file
      is always appended, never overwritten.

   IDENTIFYING TIME AND MAGNITUDE COLUMNS

      In order to load your data correctly, TS needs two pieces
      of information from each file record: time and magnitude.
      Time is the time at which a variable star observation was
      made.  Magnitude is a measure of the brightness of a star
      at a given time.

      TS expects your file to consist of columns of information,
      with blank spaces separating the columns.  Because your file
      is in a format unfamiliar to TS, you must explain the
      format.  When TS asks
              
               Time column = 1 
              
      you should enter the number of the column containing times
      (TS suggests column 1), then hit <ENTER>.  Likewise,
      when TS asks
              
               Mag. column = 2 
              
      you must enter the column number (if different from 2)
      of the magnitude column, then hit <ENTER>.

      In addition to time and magnitude, you may also load
      observer IDs.  An observer ID is a brief identifier,
      from 1 to 4 letters long, indicating who (or what) made
      a particular observation.  TS now asks
              
               Observer ID column =
              
      Enter the column number in which to find observer IDs.
      If your file doesn't have observer IDs (and most files
      won't), then simply hit <ENTER> and TS won't load any
      observer IDs.

      Because we study the evolution of a variable (the magnitude)
      as a function of time, we are studying a time series.
      Although TS is designed to analyze variable star time
      series, it can be used to load and study any kind of time
      series data.  Just enter the correct time column, and
      enter the data column as the "magnitude column," even
      'though the data may be unrelated to stellar brightness.

      One special kind of time series is an indexed time
      series.  In this case, the times are whole numbers,
      usually starting with 1.  If your data are an indexed
      time series, you may enter column 0 (zero) as the time
      column.  TS will count records as it loads data,
      and automatically assign whole numbers, starting
      with 1, as times of observation.

  CHOOSING A TIME RANGE

      The final step before TS loads the information on your star
      is the time range over which you want to view the data.  TS
      asks  (JD stands for "Julian Date").

            start JD = 0000000 

      If you want to start loading from the beginning of the data
      records, accept the default by just pressing the <ENTER> key.
      If you want to start loading from a specific date, enter that
      JD instead.  IMPORTANT NOTE: if your data file has negative
      time values, you MUST enter a (low enough) negative number
      here.  The default will start at time 0.
      
      TS also asks for the cut-off date:

            end JD = 2460000  
                                             
      If you want to load until the end of the file's data, accept
      the default (which is calendar date October 9, 1995).
      If you want to stop loading at a certain date, enter that
      JD instead.             
      
      TS begins loading as soon as you enter the end JD.  As TS
      loads, it prints blocks on the screen to let you know it's
      still working.

      The maximum number of data points that can be loaded
      at one time is 4,000.  If your star has more than 4,000
      data points available, TS tells you that its "arrays are
      full" and that it is beginning its analysis; you will
      have to look at the rest of the data during a different
      run of TS.

      If while loading you decide you've loaded enough, push
      the <ESC> key.  The program stops loading and asks
      whether you want to discontinue.  If you say <Y>, then
      TS stops loading, and works with the data it has loaded
      so far.  If you respond <N>, then it will continue its
      data loading.

      TS automatically plots after loading.

LOADING AFTER START-UP

   Push <F1>.

   Now repeat the procedure for loading at start-up.  Keep
   in mind that this time around the values that TS suggests
   for all parameters (the defaults) will be whatever you
   specified the last time you loaded data.


            *********************************
            *   III  SETTING THE DISPLAY    *
            *********************************


   DEFINING THE PARAMETERS

   The initial display shows all the data that you instructed TS
   to load.  TS leaves a bit of room on either side of the graph.
   Thus, if you load data from JD 2447000 to JD 2448400,
   there is a gap at the left end of the graph (from JD=2446900
   to JD=2447000) and at the right end (from JD=2448400 to
   JD=2448500).  TS also leaves room on the magnitude axis;
   if the data go from (lower limit)=6 to (upper limit)=15, the
   plot will range from (lower limit)=5 to (upper limit)=16.
   The display limits of JD and mag. are called the "view window."
   The view window for this example is JD=2446900 to 2448500 and
   magnitude=5 to 16.

   The text below is known as the "Standard selection menu":

============================================================================
============================================================================
<ESC>   EXIT        <F5> Time retreat    <M > place MARKER  <P > log a Point
<F1> Load Data      <F6> Time advance    <F11> bias OBServer
<F2> Average data   <F7> Zoom in/out          2447700.0000    12.3333
<F3> Polynomial fit <F8> Multilinear
<F4> Fourier        <F9> Refresh screen

N=1150     AVE=  10.0191   VAR=   4.1816   SDV=   2.0458
============================================================================
============================================================================

   CHANGING THE PARAMETERS

      Changing the limits of time

        At the top of the graph is a horizontal axis which
        shows the entire time range which you have loaded
        (plus a little extra).  At first, this entire area is
        displayed in red.  The red part of the top axis
        (the "red zone") shows how much of the total time range
        you are currently viewing.  To change the time limits
        of the view window:

         (1)Move the cursor into the top axis.

         (2)If you want to change the lower time limit, move the
             cursor near the left edge of the red zone on the
             horizontal axis at the top (the top time axis).
             Place the cursor inside the red zone, but not more
             than the width of the cursor from the edge.
             If you want to change the upper time limit, move the
             cursor near the right edge of the axis.

         (3)If you are using the mouse, click AND HOLD the left
             mouse button. 
            If you are using the keyboard, push <ENTER> once.

         (4)If you are changing the lower time limit, you will
             see beneath the screen the message                    

 Please define LOWER limit     
                               
 Move cursor to new limit,     
 then release mouse button.    
            
            If you are changing the upper time limit, you will
            see beneath the screen the message

 Please define UPPER limit    
                              
 Move cursor to new limit,    
 then release mouse button.   

         (5)Move the cursor along the top axis toward the new limit.
            You'll notice that the "red zone" moves with you.
            Just below and to the left of the bottom axis
            is a number, which changes as you move the mouse
            cursor, showing the time of the cursor's location
            on the top axis.  TS will round off the JD to the
            nearest 10- or 100-day point (depending on how
            much data there is).

         (6)When you reach the desired position,
            if you are using the mouse, release the button.
            if you are using the keyboard, push <ENTER>
             once again.

         (7)TS redraws the screen.
            The top axis is no longer completely red.  The
            part that is still red represents the time span
            for the data you're now viewing.  The blue part
            of the top axis shows the time range you're NOT
            viewing.

            Notice that the lower axis (always blue) has
            changed its limits to coincide with the limits
            of the red part of the top axis; that is, the
            red part of top axis is magnified on the bottom
            axis.

         You can also use the bottom time axis, to change the time
         limits with greater precision.

         (1)Move the cursor near the left/right edge of the
            bottom axis.

         (4)When the messages appear, their first lines say, 
            "Please refine LOWER/UPPER limit" 

         (5)A red line (which represents the red part of the top
            axis) moves with you.  The JD in the lower left corner
            will display the JD.

      Changing the limits of magnitude

      (1)Move the cursor into the "red zone" of the vertical
         axis on the left-hand side (the left magnitude axis).

      (2)If you want to change the bright magnitude limit, move
          the cursor near the top edge of the axis.
         If you want to change the faint magnitude limit, move
          the cursor near the bottom edge of the axis.

      (3)If you are using the mouse, click AND HOLD the left mouse
          button.
         If you are using the keyboard, push <ENTER> once.

      (4)If you are changing the upper limit, you will see beneath
          the screen the message

 Please define BRIGHT limit    
                               
 Move cursor to new limit,     
 then release mouse button.    

         If you are changing the lower limit, you will see beneath
          the screen the message

 Please define DIM limit    
                            
 Move cursor to new limit,  
 then release mouse button. 

      (5)Move the cursor along the axis to the new limit.
         The red zone moves with you.  Directly below the
         left axis, there is a number, which is the position
         of the cursor along the left axis.  TS displays this
         magnitude to one decimal place.

      (6)When you reach the desired position,
         if you are using the mouse, release the button.
         if you are using the keyboard, push <ENTER> once again.

      (7)TS redraws the screen. 
         The left axis is no longer completely red.  The part that
         is still red represents the magnitudes of the data you're
         now viewing; the right axis magnifies this red part.


            ******************************************
            *    IDENTIFYING AND EDITING DATA POINTS *
            ******************************************


MOVING ALONG WITH THE CURSOR

   As the cursor moves about the view window, its location
   in time and magnitude is displayed in the standard 
   selection menu.  For example,

============================================================================
============================================================================
<ESC>   EXIT        <F5> Time retreat    <M > place MARKER  <P > log a Point
<F1> Load Data      <F6> Time advance    <F11> bias OBServer
<F2> Average data   <F7> Zoom in/out          2447700.0000    12.3333
<F3> Polynomial fit <F8> Multilinear
<F4> ANOVA (period) <F9> Refresh screen

N=1150     AVE=  10.0191   VAR=   4.1816   SDV=   2.0458
============================================================================
============================================================================

   "2447700.0000" is the cursor's location on the JD axis.
   "12.3333" is its location on the magnitude axis.

IDENTIFYING DATA

   When instructed to identify a data point, TS identifies
   the point closest to the cursor, so make sure that the
   cursor is closer to the data point you're interested in
   than to any other point.  Click the left mouse button
   (if you're using the mouse) or push <ENTER> (if you're
   using the keyboard).  Now TS displays the datum's
   time and magnitude.  If you have loaded the observer ID,
   then it too will be displayed.  If there is only one
   set of initials, it indicates that there is only one
   datum at that point.  However, when there is more than
   one datum plotted at the same pixel, TS displays more
   than one set of observer initials.

EDITING DATA POINTS

   Make sure that the cursor is nearer to the point you
   want to edit than to any other.  Hit the RIGHT mouse
   button or the <BACKSPACE> key.  On some keyboards, the
   <BACKSPACE> key is marked with a left arrow, just like
   the <left-arrow> key (which is rather confusing).  The
   <BACKSPACE> key will be the left arrow just above your
   keyboard's main <ENTER> key, while the true <left-arrow>
   key will be near the other arrow keys.  In addition to
   giving the vital statistics,  the point's edit flag will
   be toggled from "good" to "bad" (or vice versa); on
   the screen, the color of the data point will change
   to reflect its new flag status.

   Whenever you toggle a data point's edit status from good
   to bad, that datum will be excluded from any further
   numerical analysis.  If you wish to bring the datum back
   into the analysis, you can simply toggle the edit status
   from bad to good.

WRITING DATA TO THE LOG FILE

   Position the cursor near the point whose information you
   want saved in the log file.  Push the "P" key.  The datum
   will be identified, and the record from the input file
   will be written to your log file.  You will also be asked
   for a "comment."  You may enter any brief comment, which
   will also be written to your log file.

THE <ESCAPE> OPTION

   Many TS functions require nontrivial amounts of
   time, especially on slower computers.  Most of TS's
   functions have an "out" via the <ESC> key, which will
   discontinue the current function.  In general, if
   you're tired of waiting, try <ESC>.


        **********************************************
        *      LOOKING (more closely) AT YOUR DATA   *
        **********************************************


ADVANCING AND RETREATING IN TIME

   <F6> moves your view window a half-frame forward in time.

   <F7> moves a half-frame backward.

   Rather than resetting the plotting limits every time you want
   to look at a different section (along the time axis) of your
   data, these functions let you step through your data; for 
   example, if you want to move forward by an entire
   frame, push <F6> twice. 

ZOOMING IN AND OUT

   1  The instant ZOOM

      If the cursor is inside the graph, then pressing
      <F7> instantly provides a 5x magnification of the
      time axis, centered on the current cursor location.
      Pushing <F7> again returns the unmagnified screen.

   2  The not-so-instant ZOOM (multiple ZOOMing)

      Move the cursor on top of the main selection menu's <F7>,
      then click the left mouse button, or, push the keyboard's
      <F7> when the cursor is outside the graph's boundaries.
      TS presents the following three options:
                                   
            <ESC> zoom back OUT                                            
            <F1> zoom-IN                                                   
            <F2> zoom-IN TIME axis ONLY 

      <F1> zooms in for a 5x magnification of both time and
       magnitude.  With the not-so-instant zooming function,
       you can continue to zoom in.  Your second zoom-in
       gives you a 25x magnification, and your third zoom-in
       gives 125x (and so on).

      <F2> magnifies the time axis 5x but leaves the magnitude
       axis unaltered (just like the instant zoom).  You can
       also continue to zoom in on only the time axis.

      <ESC> returns you to the unmagnified screen.  Although
       you can zoom in many times, you cannot progressively
       zoom out.

     After you choose which zoom function you want, the prompt

 Click mouse on center of zoom window. 

     reminds you to put the cursor in the center of the area you
     want magnified.  Then click the left mouse button (or, if
     you are not using a mouse, press <ENTER> once).

REFRESHING THE SCREEN

   Sometimes your screen can become cluttered with
   "extra" displays.  To remove the clutter, press <F9>.
   This function will clear the screen and restore the
   data display to its original state.  If your plot is
   cluttered with data averages, polynomial fits (see
   section VII), or other stuff, you can clear the clutter
   away with the <F9> function.


***********************************************
*      ANALYZING (mathematically) YOUR DATA   *
***********************************************


TS places a number of powerful mathematical tools
at your disposal.

AVERAGING THE DATA

      TS averages magnitudes (of the data in your view
      window) over a time span which you choose.
      The default time span is ten days.  If you choose
      the default, for example, then TS averages the
      magnitudes over 10-day segments.  The averages
      (and their connecting red line) are plotted on top
      of your data.

      TS also offers to plot error bars:

       A single vertical yellow line is superimposed on
       each average, showing the error limits OF THE AVERAGE
       ITSELF.  A purple line will show the 2-standard
       deviation limits of the data; most (about 95%) of
       the data should fall within these limits.

      To compute averages, press <F2>.  The first prompt is

                       Size of time slot = 10 
                          
      If you want your data averaged over each 10-day period,
      accept the default.  If you want your data averaged
      over some other period, change the default.  TS then asks 

                       Error bars? Y 

      After plotting, TS asks

                 Save these results to a file? N 

      If you answer <Y>, TS asks you to give a name to your
      file.  It then records in your file the average time,
      average magnitude, standard deviation, and number
      of data points, for each time interval covered
      by the data.

FITTING A POLYNOMIAL

      Using the method of least squares, TS can fit a
      polynomial to the data in your view window.  TS
      then computes and plots the values of the polynomial
      (which are connected by a red line, enabling you to
      see how well it fits the data).

 Starting the polynomial fit

      To fit a polynomial, push <F3>.  When you see,

                    Polynomial degree = 4

      choose a degree from 0 (fit a constant) to 20.
      Bear in mind that fitting a polynomial can take time
      if the degree is very high and there are many data
      points.

      After computing the polynomial of your chosen degree
      which best fits the data, TS presents you with the
      "polynomial menu":
         
          <ESC>   EXIT           <F5> locate MAX/min  
          <F1> Save constants                         
          <F2> Save to file                           
          <F3> Choose degree                          
          <F4> Save residuals

 Computing another polynomial with <F3>

      If you want to compute a polynomial of different
      degree, you could, of course, first hit <ESCAPE>
      to exit from the polynomial menu, then hit <F3>
      from the main menu to compute a polynomial again.
      But the easy way is simply to hit <F3> from the
      polynomial menu, and you will be asked for your
      desired new polynomial degree.

 Saving the polynomial with <F1> and <F2>

      If you want to save the actual polynomial function,
      there are two ways to do it.  One way (the brute-
      force method) is to save in a file the values of
      the polynomial function.  This is accomplished
      with the <F2> "Save to file" option.  It then saves
      to your log file the time and the value of the
      polynomial function, just as plotted on the screen
      when TS computed it.  The file will look something
      like this:
            
             POLY DEGREE 8                
             ***POWER=  44.43547950500628 
             2447012.0000  13.1958        
             2447013.0000  13.2573        
             2447014.0000  13.3120        
             2447015.0000  13.3600        
             2447016.0000  13.4016        
             .....                        
      
      After the first two lines, each line contains two
      entries: the time, and the value of the polynomial
      at that time.

      The other way to describe completely a polynomial
      is by giving its coefficients.  If you press <F1>
      when in the polynomial menu, TS will store the
      values of all the constants defining the polynomial
      to your LOG FILE.  For example, after fitting an
      8th-degree polynomial you will
      find something like this is your log file:
  
   POLY COEFFICIENTS                                                
   File=ARCHIVE  NUM=378 AVE=8.4460 SDV=1.2562 VAR=1.5738           
    JD 2447011.8000-2447359.6000 T.AVE=2447210.5948 T.VAR=4152.5427 
   Time0= 2447210.5948                                              
   Power=  44.1707093404356                                         
    0  7.770466240185926                                            
    1 -2.493150544277969D-02                                        
    2  2.433181036054912D-04                                        
    3  5.374754818997086D-06                                        
    4 -2.791269208844564D-09                                        
    5 -4.048704535525745D-10                                        
    6 -6.13585380307309D-13                                         
    7  9.44000365215379D-15                                         
    8  2.688645962586468D-17                                        
  
      After the line "Power=" are the polynomial coefficients,
      listed in scientific notation.  In the above example,
      the 0-degree coefficient is 7.770466..., the 1st-degree
      coefficient is -2.493...D-02, etc.

      The time t used in this expression is not the ordinary
      time (not the simple JD), it is the difference between
      the JD and the mid-time of all the data in the view
      window.  This mid-time is in the log file next to
      "TIME0=".  In the above example, TIME0=2447010.5948.
      To compute the polynomial function at any given time,
      we first translate the ordinary time T (the Julian
      Date) to "relative time" t with the formula

         t = T - TIME0

      Then we use this t in the usual polynomial formula.

 Computing Residuals with <F4>

      The polynomial function value is only an estimate
      (a good one, we hope!) of the true brightness of the
      star.  The difference between the observed value at
      any given moment of time and the smooth-fit value
      is the residual.  To compute residuals from the
      polynomial menu, hit <F4>.  First TS asks you to give
      a name for the file to save the residuals.  Then TS
      writes to that file a single record for each
      observation, with up to 3 entries:

  column 1. Time = Julian date.
  column 2. Residual = difference between data value
                    and the bin average.
  column 3. Observer ID (if you loaded observer IDs).

 Locating MAXima and minima with <F5>

      You can get an estimate of when the star is at
      maximum or minimum by computing the time at which
      the polynomial is at maximum or minimum.  To do so,
      from the polynomial menu, select <F5>.  Because
      a polynomial can have many maxima and many minima,
      TS needs to know which one you want to isolate.
      That's why it asks you to
      
      Please indicate the approximate MAX or min by clicking 
      the left mouse button.                                 
      
      Move the mouse cursor until its time is close to
      the time of the maximum or minimum you want to
      study.  You only have to set the cursor's time; the
      cursor's magnitude will be ignored.  Then click the
      left mouse button.

      TS finds the maximum or minimum of the polynomial
      which is nearest in time to the mouse cursor.  It then
      records to your LOG FILE the time and magnitude of that
      maximum or minimum, and marks that line of your LOG FILE
      with the phrase, "=CRIT".  Finally, TS puts a marker
      on your screen (a blue version of the mouse cursor)
      so you can see where the computed maximum or minimum lies.

FOURIER ANALYSIS

To begin Fourier analysis, press <F4>.  Then TS takes you to
the Fourier analysis menu.

Choosing the frequencies (periods) to test

To determine whether or not the data are periodic, you must
first decide which periods or frequencies you want to test.
Several of the options, namely <F1>, <F2>, and <F3>, enable
you to specify a range of periods or frequencies to test.

  a  <F1> Standard SCAN

The simplest choice is <F1>, the "standard scan."  The
smallest frequency (longest period) tested by the standard
scan is 1/4T, where T is the total time span of the data.
The standard scan will test frequencies from 1/4T to N/4T,
where N is the number of data, in steps of 1/4T.

With several thousand data points, the standard scan
requires either a very fast computer or lots of time
(although, like most TS functions, if you start it up but
can't wait until it finishes, hit <ESC> and you will be
given the option to discontinue).  You may want to use one
of the other options (see below) to test fewer frequencies.

As it tests each frequency, TS displays the frequency, period,
and power, and also records this information in your log file.
TS also plots the results, graphing frequency versus power.
Frequencies with the highest power levels are the most likely
possibilities for the actual frequency of a periodic
fluctuation in your data (if it has one; after all, not all
data are periodic).  Of course, you would like to know what
these highest-power frequencies are, and the periods that go
with them; that's why TS keeps a TABLE of the top-twenty
frequencies/periods (see below how to access the table).

<F2>, <F3>: FREQUency and PERIOD ranges

If you want to specify your own range of frequencies or periods
to test, you can choose <F2> or <F3> for the "FREQU range" or
"PERIOD range" option.  First TS asks for the low frequency or
period to test; enter the starting frequency or period.  Then
TS asks for the high frequency or period; enter the ending
frequency or period to test.  Finally TS asks for the
"resolution."  This is the spacing between test frequencies
or periods.  For instance, suppose you want to test a range
of periods, from as low as 100 days to as high as 150 days.
If you specify a resolution of 1, TS will test all periods
from 100 to 150 in 1-day steps.  Finally, when you have
specified the low and high periods or frequencies, and the
resolution, TS asks if it is AOK?  If you respond <Y> (yes),
TS performs the scan; if not, TS returns you to the Fourier
analysis menu.  TS is quite good at choosing the resolution
itself. When TS asks you for the resolution of a frequency
or period scan, if you enter 0, then TS will choose the
resolution for you automatically.

Sometimes you may wish to test only a single period or
frequency, not a whole range.  To do so, hit <F2> or <F3>.
When TS asks for the "low" period or frequency, enter the
single one you wish to test.  When it asks for the "high"
period or frequency to test, enter 0.  This signals TS that
you are not testing a range, you are only testing a single
value.  In this case, TS won't even bother to ask you for
a resolution, because it's not needed.  The "single-value"
test has another feature, that the tested period/frequency
is always stored in the "top-twenty table" (see below),
whether its power level puts it in the top twenty or not.

Modeling the data

  <F5> View TABLE

Whenever the Fourier computation finds a frequency (period)
whose power level is higher than its neighbors (i.e., when
it finds a "peak"), TS checks the power level to determine
whether or not this peak is one of the twenty best found so
far.  If so, it saves the relevant information (frequency,
period, and power level) in its top-twenty table of the
twenty best periods.  Also, whenever you test a single
period or frequency, its information is always stored in
the table.  The table only holds twenty entries, so if you
put an entry in when the table is full, the bottom table
entry will be "bumped off" -- and lost.

To view the table, select option <F5>.  TS then displays
the period and power level for the (as many as) twenty
best peaks located so far.  They are always listed in order,
from the highest power level to the lowest.  If you "bump
off" an entry when the table is full, it is always the 20th
(weakest) entry which is lost.  After you hit <F5> and the
table is displayed, TS asks

 Delete frequency #        

If you enter a number from 1 to 20, TS deletes the table entry
corresponding to your number.  This is a good way to make room
in the table for new entries, or to "clear out the clutter"
before beginning a new analysis.  If you enter a number followed 
by the "+" sign, then TS deletes the specified entry and ALL
OTHERS WHICH FOLLOW IT.  Hence if you enter

 Delete frequency # 2+

Then TS will delete table entries 2 through 20, leaving only
entry #1 in the table.  If you just hit <ENTER> or <ESC> without
giving a frequency to delete, TS returns you to the Fourier
analysis menu.

  <F6> MODEL the data

After determining the best periods, you may want to see
exactly how they match the data.  This is accomplished with
the <F6> option.  After pressing <F6>, TS displays the best-
frequency table, and asks

 Include frequency #1? Y

TS is asking which table entries you wish to use.  It
successively queries you about each frequency in the table.
If you enter a "Y" (for "Yes") then TS includes that
frequency in a multiperiodic fit to the data.
If you hit <ESC>, TS assumes that you are done selecting
frequencies, and stops asking whether to include table
frequencies.  If you enter "A" (for "All"), then TS will
include the frequency being asked about AND ALL OTHERS
WHICH FOLLOW IT.  Thus if you respond

 Include frequency #1? A

Then TS determines a multiperiodic fit using ALL the
frequencies in the top-twenty table.

When you are done specifying the frequencies to be used
in the fit, TS computes the best fit for those frequencies,
and records to the log file the parameters defining it
(the constant, and the cosine and sine coefficients for
each frequency).  It also plots the data (as white dots),
the model function constructed from your frequencies (as
a yellow line), and the residuals (as a red line).

You might want to save these residuals.  For this purpose
TS finally asks

 Save residuals to a file? N 

If you change the <N> to <Y> (yes), TS will ask you for a name
for the file.  It will then write to that file a single record
for each data point, with 5 entries:

  column 1. Time = Julian date.
  column 2. Residual = difference between data value
                    and the model function.
  column 3. Observer ID (if you loaded observer IDs).
  column 4. Original observed value.
  column 5. Model function value.

This "residual" file is a powerful tool to look for more
fluctuations in your data.  You can load the data from this
file (see the section on "loading data") and analyze it, too.


        *****************
        *   EXITING TS  *
        *****************


From the main menu, hit <ESC>.  
The program will not immediately end (in order to prevent
accidental termination).  Instead, TS asks

                         Exit? N

If you want to return to your program instead of exiting, accept
the default, which is <N> (for "No").  If you do want to exit,
change the default to <Y>.  When the program terminates, it
returns you to your original system prompt.


========================================
Please send comments or questions to:

AAVSO
25 Birch Street
Cambridge, MA 02138
========================================
