We will learn the basic tools of Fourier analysis and spectral analysis for the interpretation of geophysical processes. Emphasis is placed on understanding the concepts and mathematical methods and applying these to meteorological and oceanographic problems. Because the atmosphere and the ocean must be considered stochastic (randomly varying in time and space) in all but the largest scales, much of the course is concerned with describing stationary random processes using spectral analysis techniques. The labs are designed to put into practice the statistical and mathematical concepts presented in the lectures.

A student who successfully completes this course should be able to:

• calculate Fourier series of periodic signals;
• determine theoretically and numerically the auto correlation function and energy density (power) spectrum of a stationary random process;
• understand the concepts associated with processing discretely sampled random data of finite record length and how to apply these concepts to the design of measurement strategy;
• understand the concept of windowing and filtering and be able to apply these techniques to real data;
• determine the cross-correlation function and cross spectrum between two signals
• determine the transfer function in the frequency domain of simple linear stochastic systems as applied to physical processes and systems placed in the atmosphere and the ocean.