Fall 2020

Professor: Sarah Gille

Meetings: Monday and Wednesday: 9:30-10:50, remote

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 16 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 16 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 Canvas for slides, since they may contain copyrighted material.)

- Bia Villas Boas' github with python notebook versions of the notes
- October 2:
*No discussion* - October 5: Introduction to the course (time series, mean, variance, standard deviation, probability density functions), Homework #1
- October 7: Probability density functions (common distributions, error analysis, outliers)
- October 9:
*Discussion* - October 12: Probability density functions (error propagation, the central limit theorem, chi-squared distributions, evaluating whether data are drawn from different PDFs), Homework #2.
- October 14: Least-squares fitting (linear fits,and fitting sines and cosines)
- October 16:
*Discussion.*Field trip. Meet at the entrance to the pier at 9:30 am. - October 19: Introducing the Fourier transform (chi-squared fitting, Nyquist frequency, cosine and sine transformations) Homework #3
- October 21: Fourier transform notation, great traits of the Fourier transform
- October 23:
*Discussion* - October 26: Parseval's theorem and computing spectra, Homework #4
- October 28: Spectra, error bars on spectra
- October 30:
*Discussion* - November 2: More on error bars, normalization, and the sinc function, Homework #5 (due Monday, November 9)
- November 4: More on windowing, and degrees of freedom
- November 6:
*Discussion* - November 9: Aliasing, Homework #6
- November 11:
*holiday*, no class. - November 13:
*Discussion* - November 16: Alternatives to segmenting to compute spectra: averaging in frequency, spectra from the autocovariance., Homework #7
- November 18: Frequency-wavenumber spectra, variance preserving spectra
- November 20:
*Discussion* - November 23: Correlation and coherence, Homework #8
- November 25: Correlation and coherence (part 2)
- November 27:
*Thanksgiving break---no class* - November 30: Coherence: Uncertainties and some practical examples, Final Homework
- December 2: Transfer function, salinity spiking, coherence and transfer functions with noise
- December 4:
*Discussion* - December 7: Multi-taper spectra
- December 9: Course themes and conclusions
- December 11:
*Discussion:* - December 16:
*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