HW7

Please print off your solutions and turn them in the usual way. Make sure your name is on the printout the work is your own.

tiltmeter dataset

Save this file to your local space. It has 12468 lines of the form:

2339 278.000
2340 278.000
2341 279.000
2342 280.000
2343 280.000
2344 281.000
2345 282.000
2346 282.000
2347 283.000

The first column is time (in some units) and the second is tilt in nanoradians. If I tell you that there are 50 days worth of data, you can figure out dt (the time between samples. Then the Nyquist frequency is 1/(2 dt).

1)  Write a mathematica program to read in the data.
2)  Compute the discrete (i.e., fast) fourier transform
3)  Plot the absolute value of the fourier transform.  The x-axis should be frequency, not sample numbers.
4)  Zoom your plot into the interesting part I showed in class.  Namely the diurnal and semi-diurnal tides.
5)  Each of the tidal peak is split into two peaks separated by some small frequency.   This is the frequency domain signature of a beating pattern.  Compute these two frequency shifts and label your plot with the frequencies of each of the 4 peaks (2 diurnal and 2 semi-diurnal).

To get the best looking peaks for the tides it is useful to remove the large DC component. So try subtracting off the mean. You might even try subtracting off the linear trend as well.

Hint: There are likely many ways to read in the file. I used OpenRead and Read.