Fall 2017

Professor: Sarah Gille

Meetings: Tuesday and Thursday: 11:00-12:20, 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 exam is scheduled to be held Wednesday 13 December, 11:30-2:30. We will plan to use this time slot for final presentations related to the final assignment.

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.)

- September 28: Introduction to the course (time series, mean, variance, standard deviation, probability density functions), Homework #1
- October 3: Probability density functions (common distributions, error analysis, outliers)
- October 5: Probability density functions (error propagation, the central limit theorem, chi-squared distributions, evaluating whether data are drawn from different PDFs) Homework #2
- October 10: Field trip. Melissa Carter will show us the data collection system on the Scripps pier. Meet at the base of the pier at 11 am.
- October 12: Least-squares fitting (linear fits, fitting sinusoids, Nyquist frequency), Homework #3
- October 17: Introducing the Fourier transform (chi-squared fitting, cosine and sine transformations, notation for Fourier transforms)
- October 19: Great traits of the Fourier transform, Homework #4
- October 24: Matthew Alford, guest lecture, Parseval's theorem and computing spectra
- October 26: no class, Homework #5
- October 31: Error bars on spectra
- November 2: Windowing, and the sinc function, Homework #6
- November 7: Alternatives to segmenting to compute spectra: averaging in frequency, spectra from the autocovariance, plus units for the y-axis.
- November 9: More on the autocovariance, variance preserving spectra, Homework #7
- November 14: Matthew Alford, guest lecture, Aliasing
- November 16: Matthew Alford, guest lecture, Frequency-wavenumber spectra
- November 21: Correlation and coherence, Homework #8
- November 28: Coherence: Some practical examples
- November 30: Coherence uncertainties, Homework #9
- December 5: Coherence with noise, and cross-covariance
- December 7: Transfer functions, salinity spiking and synthesizing course themes

- 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