Fall 2021

Professor: Sarah Gille

Meetings: Monday and Wednesday: 8:30-9:50, Spiess 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 (Monday 6 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 Monday 6 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
- September 24:
*No discussion* - September 27: Introduction to the course (time series, mean, variance, standard deviation, probability density functions) Homework #1
- September 29: Probability density functions (common distributions, error analysis, outliers)
- October 1:
*Discussion* - October 4: Probability density functions (error propagation, the central limit theorem, chi-squared distributions, evaluating whether data are drawn from different PDFs) Homework #2.
- October 6: Least-squares fitting (linear fits,and fitting sines and cosines)
- October 8:
*Discussion.* - October 11: Introducing the Fourier transform (chi-squared fitting, Nyquist frequency, cosine and sine transformations) Homework #3
- October 13: Fourier transform notation, great traits of the Fourier transform
- October 15:
*Field trip to the SIO Pier with Melissa Carter: Meet at the entrance to the pier at 9 am.* - October 18: Parseval's theorem and computing spectra
- October 20: Spectra, error bars on spectra
- October 22:
*Discussion* - October 25: More on error bars, normalization, and the sinc function
- October 27: More on windowing, and degrees of freedom
- October 29:
*Discussion* - November 1: Aliasing
- November 3: Alternatives to segmenting to compute spectra: averaging in frequency, spectra from the autocovariance.
- November 5:
*Discussion* - November 8: Frequency-wavenumber spectra, variance preserving spectra
- November 10: Correlation and coherence
- November 12:
*Discussion* - November 15: Correlation and coherence (part 2)
- November 17: Coherence: Uncertainties and some practical examples
- November 19:
*Discussion* - November 22: Transfer function, salinity spiking, coherence and transfer functions with noise
- November 24: Transfer function, salinity spiking, coherence and transfer functions with noise
- November 26:
*Thanksgiving break---no class* - November 29: Multi-taper spectra
- December 1: Course themes and conclusions
- December 3:
*Discussion:* - December 6:
*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