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Lesson Plans: Time that Star! (Day 2)

Time That Star!

Day 2 Sample of Epoch Folding

Stopwatch

Summary

You are presented with a data sample set for the intensity of a signal over time. Can you determine if there is periodic behavior evident in the data? If so, what is the period? You'll use a technique called "Epoch Folding" to answer these questions

Procedure

You are given the following data set for intensity (in increments of 100,000) over time (in months). Using the steps given below, you will find the true, mathematical period through a method called Epoch Folding.

Time 1 2 3 4 5 6 7 8 9 10 11 12
Intensity 11 9 7 5 3 1 3 5 7 9 11 9
Time 13 14 15 16 17 18 19 20 21 22 23 24
Intensity 7 5 3 1 3 5 7 9 11 9 7 5
  1. Create a line plot on graph paper.
  2. Guess the length of the period.
  3. Locate the section of the plot for your guess of a period, starting with the smallest time on the x-axis. Color over the line it makes with a red pencil.
  4. Locate the next period segment which should be an exact and adjacent match to the curve of the first period. Color over the line the second period makes with a blue pencil.
  5. graph of sample data
  6. Starting from the left end of the x-axis, find the 1st data point on the red curve and the 1st data point on the blue curve and determine the mean of their y values (in this case, intensity is the y value). For this first data point, we will call its x-axis value "Time Bin #1".

    Continue to do this with the remaining points on the curves, calling the x-axis values "Time Bin #2", "Time Bin #3", etc. and associating the y value of mean with the x value "Time Bin".

  7. first two locations on adjacent curves

    The two black dots represent the first locations on adjacent curves. The white squares represent the second two.

  8. Create a chart that looks like this and import the appropriate, calculated data.
  9. Time BinIntensity
    1 
    2 
    3 
    4 
    5 
    6 
    7 
    8 
    9 
    etc. 
  10. Plot the data from that chart.
  11. Does it make a curve? Does it resemble the plot of your guessed period? If so, you have the period!
  12. Folded time chart (correct period guess)
  13. Does it make a straight line, or an approximate straight line? If so, the period you guessed is wrong and you need to go back to step one of the Epoch Folding instructions and begin again.
  14. Folded time chart (incorrect period guess)
  15. This method can be used with any periodic data set, though most data sets won't be as clean as this sample set!



 

A service of the High Energy Astrophysics Science Archive Research Center (HEASARC), Dr. Alan Smale (Director), within the Astrophysics Science Division (ASD) at NASA/GSFC

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