This module introduces characteristic functions.
This module describes the circular convolution algorithm and an alternative algorithm
The module looks at circular shifting and how it is can be used as a tool to represent the shifting of a periodic sequence.
The first portion of the class will cover topics in analog communication. Beginning with basic Fourier transform properties, techniques for analog modulation and demodulation will be developed. Insights to these problems will be uncovered along the way. The rest of the course will be devoted digital communication.
Review of the continuous-time fourier transform.
Details the Continuous-Time Fourier Transform.
How to compute discrete-time Fourier transforms for decaying sequences.
This module shows how to derive the scintillating and useful Fourier transform.
The course covers the basic techniques for evaluating the maximum forces and loads over the life of a marine structure or vehicle, so as to be able to design its basic configuration. Loads and motions of small and large structures and their short-term and long-term statistics are studied in detail and many applications are presented in class and studied in homework and laboratory sessions. Issues related to seakeeping of ships are studied in detail. The basic equations and issues of maneuvering are introduced at the end of the course. Three laboratory sessions demonstrate the phenomena studied and provide experience with experimental methods and data processing.
This course covers the design, construction, and testing of field robotic systems, through team projects with each student responsible for a specific subsystem. Projects focus on electronics, instrumentation, and machine elements. Design for operation in uncertain conditions is a focus point, with ocean waves and marine structures as a central theme. Topics include basic statistics, linear systems, Fourier transforms, random processes, spectra, ethics in engineering practice, and extreme events with applications in design.
This is the first semester of a two-semester sequence on Differential Analysis. Topics include fundamental solutions for elliptic; hyperbolic and parabolic differential operators; method of characteristics; review of Lebesgue integration; distributions; fourier transform; homogeneous distributions; asymptotic methods.
The Dirichlet conditions are the sufficient conditions to guarantee existence and convergence of the Fourier series or the Fourier transform.
The Fourier transform can be computed in discrete-time despite the complications caused by a finite signal and continuous frequency.
Average stock price as an example of discrete-time filtering.
Computing the Fourier Transform is made simpler by the symmetry of the signal's conjugate and the properties of real-valued signals.
Details the discrete-time fourier transform.
Discussion of Discrete-time Fourier Transforms. Topics include comparison with analog transforms and discussion of Parseval's theorem.
Computing discrete-time frequencies by the use of Fourier transforms.
Gives various Fourier transform properties
The module will provide analysis and examples of how a continuous-time signal is converted to a digital signal and processed.
