Nyquist Criterion
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This course serves as an introduction to the theory and practice behind many of today's communications systems. 6.450 forms the first of a two-course sequence on digital communication. The second class, 6.451, is offered in the spring. Topics covered include: digital communications at the block diagram level, data compression, Lempel-Ziv algorithm, scalar and vector quantization, sampling and aliasing, the Nyquist criterion, PAM and
Addendum: Hit-And-Run CG Algorithm, Maximum Volume Ellipsoid Method, Chebyshev Center Method, Analytic Center Cutting-Plane Method, Extensions (Of Cutting-Plane Methods), Dropping Constraints, Epigraph Cutting-Plane Method, PWL Lower Bound On Convex Function, Lower Bound, Analytic Center Cutting-Plane Method, ACCPM Algorithm, Constructing Cutting-Planes, Computing The Analytic Center, Infeasible Start Newton Method Algorithm, Properties...more
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Recap: Ellipsoid Method, Improvements (To Ellipsoid Method), Proof Of Convergence, Interpretation Of Complexity, Deep Cut Ellipsoid Method, Ellipsoid Method With Deep Objective Cuts, Inequality Constrained Problems, Stopping Criterion, Epigraph Ellipsoid Method, Epigraph Ellipsoid Example, Summary: Methods For Handling, Nondifferentiable Convex Optimization Problems Directly, Decomposition Methods, Separable Problem, Complicating...more
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Example: Piecewise Linear Minimization, ACCPM With Constraint Dropping, Epigraph ACCPM, Motivation (For Ellipsoid Method), Ellipsoid Algorithm For Minimizing Convex Function, Properties Of Ellipsoid Method, Example (Using Ellipsoid Method), Updating The Ellipsoid, Simple Stopping Criterion, Basic Ellipsoid Algorithm, Interpretation (Of Basic Ellipsoid Algorithm), Example (Of Ellipsoid Method)
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Review Of Sampling And Interpolation Results, Terminology: Sampling Rate, Nyquist Rate, Issues With The Interpolation Formula In Practical Applications, Aliasing And Interpolation, Main Argument In Aliasing, Example Of Aliasing: Cosine
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Optimal And Locally Optimal Points, Feasibility Problem, Convex Optimization Problem, Local And Global Optima, Optimality Criterion For Differentiable F0, Equivalent Convex Problems, Quasiconvex Optimization, Problem Families, Linear Program
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Convergence Proof, Stopping Criterion, Example: Piecewise Linear Minimization, Optimal Step Size When F* Is Known, Finding A Point In The Intersection Of Convex Sets, Alternating Projections, Example: Positive Semidefinite Matrix Completion, Speeding Up Subgradient Methods, A Couple Of Speedup Algorithms, Subgradient Methods For Constrained Problems, Projected Subgradient Method, Linear Equality Constraints, Example: Least L_1-Norm
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Nyquist theory, pulse amplitude modulation (PAM), quadrature amplitude modulation (QAM), and frequency translation
