Fall 2018

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 in class, either in the last week during class on December 3 or discussion section December 5. We will not meet during the final exam time slot (Wednesday 12 December, 8:00-11:00), but your final write up of your project will be due no later than 11 am on Wednesday 12 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.)

- September 28:
*No discussion* - October 1: 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:
*No discussion* - October 8: Probability density functions (error propagation, the central limit theorem, chi-squared distributions, evaluating whether data are drawn from different PDFs) Homework #2
- October 10: Least-squares fitting (linear fits, fitting sinusoids)
- October 12:
*Discussion.*Field trip. Melissa Carter will show us the data collection system on the Scripps pier. Meet at the base of the pier at 9:30 am. - October 15: Introducing the Fourier transform (chi-squared fitting, Nyquist frequency, cosine and sine transformations), Homework #3
- October 17: Fourier transform notation, great traits of the Fourier transform
- October 19:
*Discussion* - October 22: Parseval's theorem and computing spectra, Homework #4
- October 24: Spectra, error bars on spectra
- October 26:
*Discussion* - October 29:
*Guest lecture, Matthew Alford:*Aliasing, Homework #5 (due Wednesday, November 7) - October 31: More on aliasing, windowing, and the sinc function
- November 2:
*Discussion* - November 5: Degrees of freedom for spectra with overlapping segments
- November 7: Alternatives to segmenting to compute spectra: averaging in frequency, spectra from the autocovariance. Homework #6 (midterm, independent assignment)
- November 9:
*Discussion* - November 12:
*holiday*, no class. - November 14: More on the autocovariance, introduction to frequency-wavenumber spectra
- November 16:
*Discussion* - November 19: Frequency-wavenumber spectra
- November 21: Correlation and coherence, Final Homework
- November 23:
*No discussion---Happy Thanksgiving!* - November 26: Coherence: Uncertainties and some practical examples
- November 28: Variance preserving spectra, cross-covariance, transfer functions
- November 30:
*Discussion* - December 3: Coherence with noise, and cross-covariance, transfer functions, salinity spiking, synthesizing course themes
- December 5: Final project presentations, Part I
- December 7:
*Discussion:*Final project presentations Part II

- 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

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