- Abstract:
-
Introduction to the continuous-time Fourier Transform.
- Subject:
- Mathematics and Statistics, Science and Technology
- Grade Level:
- Post-secondary
- Collection:
- Connexions
Introduction to the continuous-time Fourier Transform.
This course gives an outline of the Discrete Fourier Transform and an in-depth look at the Fast Fourier Transform. Many different ways of speeding up a discrete Fourier Transform are examined and evaluated for how efficient they are.
In this class, food serves as both the subject and the object of historical analysis. As a subject, food has been transformed over the last 100 years, largely as a result of ever more elaborate scientific and technological innovations. From a need to preserve surplus foods for leaner times grew an elaborate array of techniques -- drying, freezing, canning, salting, etc -- that changed not only what people ate, but how far they could/had to travel, the space in which they lived, their relations with neighbors and relatives, and most of all, their place in the economic order of things. The role of capitalism in supporting and extending food preservation and development was fundamental. As an object, food offers us a way into cultural, political, economic, and techno-scientific history. Long ignored by historians of science and technology, food offers a rich source for exploring, e.g., the creation and maintenance of mass-production techniques, industrial farming initiatives, the politics of consumption, vertical integration of business firms, globalization, changing race and gender identities, labor movements, and so forth. How is food different in these contexts, from other sorts of industrial goods? What does the trip from farm to table tell us about American culture and history?
Introduces the fact that the diffraction pattern through an aperture is the Fourier transform of the aperture.
This module will introduce the Fourier Series and its Fourier coefficients using the concepts of eigenfunctions and basis. We will show several examples of how to decompose a signal and find the Fourier coefficients.
This module calculates the Fourier transform of the pulse signal.
This report summarizes work done as part of the Wavelet Based Image Analysis PFUG under Rice University's VIGRE program. VIGRE is a program of Vertically Integrated Grants for Research and Education in the Mathematical Sciences under the direction of the National Science Foundation. A PFUG is a group of Postdocs, Faculty, Undergraduates and Graduate students formed round the study of a common problem.
This module introduces the redundant discrete wavelet transform as well as two level dependent estimators that could potentially be used for image denoising, the Bishrink algorithm and the Bayesian Least Squares-Gaussian Scale Mixture algorithm. A simulation designed to evaluate the efficacies of each of these methods for the purpose of denoising astronomical image data is described, and its results are presented and discussed.
This Connexions module describes work conducted as part of Rice University's VIGRE program, supported by National Science Foundation grant DMS?0739420.
This module explains the inverse Fourier transform.
Properties of Laplace Transforms
This module discusses how the Spatial Transform is accomplished.