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Keywords: Fourier Series
(Complete Item Description)
- Abstract: This module looks at the basic circular convolution relationship between two sets of Fourier coefficients.
- Subject:
Mathematics and Statistics, Science and Technology
- Grade Level:
Post-secondary
- Collection:
Connexions
(Complete Item Description)
- Abstract: Signals can be composed by a superposition of an infinite number of sine and cosine functions. The coefficients of the superposition depend on the signal being represented and are equivalent to knowing the function itself.
- Subject:
Mathematics and Statistics, Science and Technology
- Grade Level:
Post-secondary
- Collection:
Connexions
(Complete Item Description)
- Abstract: This module discusses the covergence of the Fourier Series to show that it can be a very good approximation for all signals.
- Subject:
Science and Technology
- Grade Level:
Post-secondary
- Collection:
Connexions
(Complete Item Description)
- Abstract: The module goes through the steps of deriving the Fourier coefficient equation from the general Fourier series equation.
- Subject:
Mathematics and Statistics
- Grade Level:
Post-secondary
- Collection:
Connexions
(Complete Item Description)
- Abstract: This module shows how to derive the scintillating and useful Fourier transform.
- Subject:
Mathematics and Statistics, Science and Technology
- Grade Level:
Post-secondary
- Collection:
Connexions
(Complete Item Description)
- Abstract: Study of ordinary differential equations, including modeling of physical problems and interpretation of their solutions. Standard solution methods for single first-order equations, including graphical and numerical methods. Higher-order forced linear equations with constant coefficients. Complex numbers and exponentials. Matrix methods for first-order linear systems with constant coefficients. Non-linear autonomous systems; phase plane analysis. Fourier series; Laplace transforms.
- Subject:
Mathematics and Statistics
- Grade Level:
Post-secondary
- Collection:
MIT OpenCourseWare
(Complete Item Description)
- Abstract: Study of ordinary differential equations, including modeling of physical problems and interpretation of their solutions. Standard solution methods for single first-order equations, including graphical and numerical methods. Higher-order forced linear equations with constant coefficients. Complex numbers and exponentials. Matrix methods for first-order linear systems with constant coefficients. Non-linear autonomous systems; phase plane analysis. Fourier series; Laplace transforms.
- Subject:
Mathematics and Statistics
- Grade Level:
Post-secondary
- Collection:
MIT OpenCourseWare
(Complete Item Description)
- Abstract: The Dirichlet conditions are the sufficient conditions to guarantee existence and convergence of the Fourier series or the Fourier transform.
- Subject:
Mathematics and Statistics
- Grade Level:
Post-secondary
- Collection:
Connexions
(Complete Item Description)
- Abstract: This module defines eigenvalues and eigenvectors and explains a method of finding them given a matrix. These ideas are presented, along with many examples, in hopes of leading up to an understanding of the Fourier Series.
- Subject:
Science and Technology
- Grade Level:
Post-secondary
- Collection:
Connexions
(Complete Item Description)
- Abstract: This module defines eigenvalues and eigenvectors and explains a method of finding them given a matrix. These ideas are presented, along with many examples, in hopes of leading up to an understanding of the Fourier Series.
- Subject:
Mathematics and Statistics
- Grade Level:
Post-secondary
- Collection:
Connexions
(Complete Item Description)
- Abstract: This module discusses signal equality. It looks at Gibb's phenomenon, and defines equality in the mean square and pointwise.
- Subject:
Science and Technology
- Grade Level:
Post-secondary
- Collection:
Connexions
(Complete Item Description)
- Abstract: Explore the forces at work when you try to push a filing cabinet. Create an applied force and see the resulting friction force and total force acting on the cabinet. Charts show the forces, position, velocity, and acceleration vs. time. View a Free Body Diagram of all the forces (including gravitational and normal forces).
(Complete Item Description)
- Abstract: Continues 18.100. Roughly half the subject devoted to the theory of the Lebesgue integral with applications to probability, and half to Fourier series and Fourier integrals.
- Subject:
Mathematics and Statistics
- Grade Level:
Post-secondary
- Collection:
MIT OpenCourseWare
(Complete Item Description)
- Abstract: This module derives the Discrete-Time Fourier Series (DTFS), which is a fourier series type expansion for discrete-time, periodic functions. The module also takes some time to review complex sinusoids which will be used as our basis.
- Subject:
Mathematics and Statistics, Science and Technology
- Grade Level:
Post-secondary
- Collection:
Connexions
(Complete Item Description)
- Abstract: A brief introduction to Fourier Series starting from the normal modes of an oscillating string. The concept is then extended to Fourier's integral theorem.
- Subject:
Science and Technology
- Grade Level:
Post-secondary
- Collection:
Connexions
(Complete Item Description)
- Abstract: Shows how to use Fourier series to approximate a square wave, as opposed to the sinusoidal waves seen previously.
- Subject:
Science and Technology
- Grade Level:
Post-secondary
- Collection:
Connexions
(Complete Item Description)
- Abstract: This module will give a brief over of the key concepts involving the Fourier series and the tools used to decompose and approximate a given signal.
- Subject:
Mathematics and Statistics, Science and Technology
- Grade Level:
Post-secondary
- Collection:
Connexions
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