Scalar Quantization
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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
Logistics, Convex Functions, Examples, Restriction Of A Convex Function To A Line, First-Order Condition, Examples (FOC And SOC), Epigraph And Sublevel Set, Jensen's Inequality, Operations That Preserve Convexity, Pointwise Maximum, Pointwise Maximum, Composition With Scalar Functions, Vector Composition
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Showing that, unlike line integrals of scalar fields, line integrals over vector fields are path direction dependent.
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Showing that if a vector field is the gradient of a scalar field, then its line integral is path independent.
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Review C Control Structures, Scalar Data Types, Representaton of Integers
Berkeley / Computer Science
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Showing that the line integral of a scalar field is independent of path direction.
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Intuition of the gradient of a scalar field (temperature in a room) in 3 dimensions.
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Quantization
