Inspiring and Motivating Individuals
Diagnose and solve motivation problems so that you can bring out the best in your people.
The Architectural Imagination
How to read, analyze, and understand different forms of architectural representation
Social and historical contexts behind major works of architecture
Basic principles to produce your own architectural drawings and models
Pertinent content for academic study or a professional career as an architect
The Estimation of Frequency
Periodic phenomena occur naturally. Often the periods are obvious. For example, hourly temperature data are expected to have approximate periods of length 24 and 24*365.25 hours approximately. These periods are only approximate, as there is always going to be some variation that is impossible to model deterministically. Often the periodicity or frequency is unknown, and its value crucial to the understanding of the phenomenon. It therefore needs to be estimated from data.
The estimation of frequency from data had occupied scientists since the eighteenth century. The periodogram was introduced by Schuster in 1898 as a means of estimating a `hidden' periodicity, but other techniques were available by then. In particular, the Buys-Ballot method was introduced in 1847. Indeed, Gauss developed an FFT-like technique in about 1805. The statistical theory of the properties of estimators appears to have been evaluated first by Whittle in 1952, who noted that the relevant Cramer-Rao lower bound for frequency was of order T^{-3}, rather than the usual T^{-1}, where T is the sample size. Walker (1971) and Hannan (1975) followed up with rigorous results and proofs for the case where the additive noise has very general properties.
The publication of the Cooley and Tukey FFT algorithm in 1965 has undoubtedly been responsible for the enormous interest in `frequency domain' techniques - those based on the Fourier transforms of data rather than the data themselves. Large numbers of articles have appeared, mainly in the signal processing literature, but also in statistical journals.
In this course, we shall examine many different frequency estimation techniques and establish the asymptotic properties of the estimators. All of the probabilistic and estimation theory needed will be introduced to establish the (strong) consistency and central limit theorems of the estimators. We shall also consider the computational aspects of the algorithms, and use Matlab code to implement them.
Tangible Things
Gain an understanding of history, museum studies, and curation by looking at, organizing, and interpreting art, artifacts, scientific curiosities, and the stuff of everyday life.
Understanding of museum curation approaches
The basics of historical analysis and interpretation
A sense of the work that historians, curators, and collectors perform
Strong critical thinking and analytical skills
How things that seem to belong to different disciplines actually can “talk” to one another
How close looking at even a single object can push beyond academic and disciplinary boundaries