Fall 2019

Professor: Sarah Gille

Meetings: Monday and Wednesday: 9:30-10:50, Spiess Hall 330

Course Requirements: Complete weekly problem sets. For most of the problem sets, you may work collaboratively, though the work that you submit must be your own. (Please follow the standards of scientific publication and identify your collaborators.) A midterm and final problem must be completed independently. (They will have about the same scope as the the other problem sets.)

The final problem set will be an independent project, which you will present during the final exam time slot (Wednesday 11 December, 8:00-11:00). A draft write up will be due during the final week of classes, and the final write up of your project will be due no later than 11 am on Wednesday 11 December.

To gain from this class, students are expected to come to class, participate in class discussions, ask questions. There will be some assigned reading (available in electronic form), and students are expected to complete the reading.

Syllabus

Resources:

Lecture notes and handouts: (See TritonED for slides, since they may contain copyrighted material.)

- Bia Villas Boas' github with python notebook versions of the notes
- September 27:
*No discussion* - September 30: Introduction to the course (time series, mean, variance, standard deviation, probability density functions), Homework #1
- October 2: Probability density functions (common distributions, error analysis, outliers)
- October 4:
*Discussion* - October 7: Probability density functions (error propagation, the central limit theorem, chi-squared distributions, evaluating whether data are drawn from different PDFs), Homework #2. Updated links to temperature and salinity data. Note that the Shore Stations program would like to log their users via this form.
- October 9: Field trip. Meet at the entrance to the pier at 9:30 am.
- October 11:
*Discussion.* - October 14: Least-squares fitting (linear fits, fitting sinusoids), Homework #3
- October 16: Introducing the Fourier transform (chi-squared fitting, Nyquist frequency, cosine and sine transformations)
- October 18:
*Discussion* - October 21: Fourier transform notation, great traits of the Fourier transform, Homework #4
- October 23: Parseval's theorem and computing spectra
- October 25:
*Discussion* - October 28: Spectra, error bars on spectra, Homework #5 (due Monday, November 4)
- October 30: More on error bars, normalization, and the sinc function
- November 1:
*Discussion* - November 4: More on windowing, and degrees of freedom, Homework #6 (due Wednesday, November 13)
- November 6: Aliasing
- November 8:
*Discussion* - November 11:
*holiday*, no class. - November 13: Alternatives to segmenting to compute spectra: averaging in frequency, spectra from the autocovariance. Homework #7 (due Wednesday, November 20)
- November 15:
*Discussion* - November 18: Frequency-wavenumber spectra, variance preserving spectra
- November 20: Correlation and coherence, Homework #8 (due Monday, December 2)
- November 22:
*Discussion* - November 25: Coherence: Uncertainties and some practical examples, Final Homework
- November 27: Building intuition for spectra and coherence
- November 30:
*Thanksgiving---no class* - December 2: Transfer function, salinity spiking, coherence and transfer functions with noise
- December 4: Multi-taper spectra, course themes and conclusions
- December 6:
*Discussion:* - December 11:
*Final exam:*Student presentations

- Introduction: statistics, probability density functions, mean, standard deviation, skewness, kurtosis
- Error propagation
- Least-squares fitting
- The Fourier transform
- Spectra, spectral uncertainties, using Monte Carlo methods (and fake data) to evaluate formal uncertainties
- Windowing and filtering
- Cross-spectra, coherence, uncertainties of coherence
- Multi-dimensional spectral analysis

- Rotary spectra
- Alternative approaches for computing spectra: multitaper and maximum entropy methods
- Filter design
- Introduction to linear systems
- Spectral modeling; spectral physics

Sarah Gille's Home Page