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Discrete-Time Signals (m0009)
Author: Don Johnson
Maintainers: Don Johnson, Roy Ha, Benjamin Fite, Mariyah Poonawala, Prashant Singh, Matthew Hutchinson
Keywords: alphabet, complex, complex-valued, decompose, discrete-time, exponential, real-valued, sequences, signals, sine, sinusoid, symbolic-valued signals, systems, unit sample
Summary: Signals can be represented by discrete quantities instead of as a function of a continuous variable. These discrete time signals do not necessarily have to take real number values. Many properties of continuous valued signals transfer almost directly to the discrete domain.
Subject: Science and Technology
Language: English
Popularity: 97.51%
Revised: 2009-06-04
Revisions: 25
Discrete-Time Systems in the Time-Domain (m10251)
Author: Don Johnson
Maintainers: Don Johnson, CJ Ganier, John Cottrell, Matthew Hutchinson
Keywords: difference equation, digital signal processing, discrete-time systems, DSP, shift-invariant systems, superposition, time domain
Summary: Discrete-time systems allow for mathematically specified processes like the difference equation.
Subject: Science and Technology
Language: English
Popularity: 93.41%
Revised: 2013-05-18
Revisions: 26
Eigenvectors and Eigenvalues (m10736)
Maintainers: Michael Haag, Justin Romberg, Richard Baraniuk, Mariyah Poonawala, Prashant Singh, Matthew Hutchinson
Keywords: determinant, eigenfunction, eigenvalue, eigenvalues, eigenvector, fourier, fourier series, linear system
Summary: 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
Language: English
Popularity: 99.18%
Revised: 2010-07-29
Revisions: 9
Fourier Series Wrap-Up (m10749)
Maintainers: Michael Haag, Justin Romberg, Richard Baraniuk, Mariyah Poonawala, Prashant Singh, Matthew Hutchinson
Keywords: fourier, fourier series, signal, system
Summary: (Blank Abstract)
Subject: Mathematics and Statistics
Language: English
Popularity: 76.10%
Revised: 2010-07-29
Revisions: 7
Fourier Series: Eigenfunction Approach (m10496)
Maintainers: Justin Romberg, Richard Baraniuk, Michael Haag, Mariyah Poonawala, Prashant Singh, Matthew Hutchinson
Keywords: coefficient, eigenfunctions, fourier, fourier coefficients, fourier series, inverse transform, LTI, LTI system, signals, transform
Summary: 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.
Subject: Mathematics and Statistics
Language: English
Popularity: 95.82%
Revised: 2010-07-29
Revisions: 24
Gibbs Phenomena (m10092)
Maintainers: Ricardo Radaelli-Sanchez, Mariyah Poonawala, Prashant Singh, Justin Romberg, Melissa Selik, Matthew Hutchinson, Dan Calderon
Keywords: almost everywhere, fourier series, gibbs phenomenon, nonuniform convergence
Summary: The Fourier Series is the representation of continuous-time, periodic signals in terms of complex exponentials. The Dirichlet conditions suggest that discontinuous signals may have a Fourier Series representation so long as there are a finite number of discontinuities. This seems counter-intuitive, however, as complex exponentials are continuous functions ... of discontinuities.
Subject: Science and Technology
Language: English
Popularity: 96.79%
Revised: 2011-09-29
Revisions: 15
Haar Wavelet Basis (m10764)
Maintainers: Mariyah Poonawala, Prashant Singh, Matthew Hutchinson, Dan Calderon
Keywords: basis, expansion, fourier, fourier series, haar, haar wavelet, hilbert, hilbert spaces, wavelet, wavelets
Summary: This module gives an overview of wavelets and their usefulness as a basis in image processing. In particular we look at the properties of the Haar wavelet basis.
Subject: Science and Technology
Language: English
Popularity: 97.72%
Revised: 2011-09-02
Revisions: 10
Inner Products (m10755)
Maintainers: Michael Haag, Justin Romberg, Richard Baraniuk, Mariyah Poonawala, Prashant Singh, Matthew Hutchinson
Keywords: dot product, inner product, inner products, norm, orthogonal, projection
Summary: This module describes the concept of inner products, which leads into our introduction of Hilbert spaces. Examples and properties of both of these concepts are discussed.
Subject: Mathematics and Statistics
Language: English
Popularity: 91.87%
Revised: 2010-07-29
Revisions: 9
Linear Algebra: The Basics (m10734)
Maintainers: Michael Haag, Justin Romberg, Richard Baraniuk, Mariyah Poonawala, Prashant Singh, Matthew Hutchinson
Keywords: bases, basis, independence, linear algebra, linear independence, span
Summary: This module will give a very brief tutorial on some of the basic terms and ideas of linear algebra. These will include linear independence, span, and basis.
Subject: Mathematics and Statistics
Language: English
Popularity: 98.39%
Revised: 2010-07-29
Revisions: 7
Matrix Diagonalization (m10738)
Author: Michael Haag
Maintainers: Mariyah Poonawala, Prashant Singh, Matthew Hutchinson
Summary: (Blank Abstract)
Subject: Mathematics and Statistics
Language: English
Popularity: 86.61%
Revised: 2010-07-29
Revisions: 7
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Total Collections: 1326
Total Modules: 22026