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Description: This lecture starts with how to define useful subproblems for strings or sequences, and then looks at parenthesization, edit distance, and the knapsack problem. The lecture ends with a brief discussion of pseudopolynomial time. Instructor: Erik Demaine
Description: This lecture covers open addressing, which is another approach to dealing with collisions (hashing with chaining was covered in Lecture 8). Cryptographic hashing is also introduced. Instructor: Srini Devadas
Description: This lecture covers depth-first search, including edge classification, and how DFS is used for cycle detection and topological sort. Instructor: Erik Demaine
Description: This lecture introduces weighted graphs and considers general approaches to the shortest paths problem. The lecture discusses single source shortest paths, negative-weight edges, and optimal substructure. Instructor: Srini Devadas
Description: This lecture introduces dynamic programming, in which careful exhaustive search can be used to design polynomial-time algorithms. The Fibonacci and shortest paths problems are used to introduce guessing, memoization, and reusing solutions to subproblems. ...
Description: This recitation covers several practice problems for Quiz 1, taken from previous semesters of 6.006. Instructor: Victor Costan
Instructor: Dennis Freeman Description: Three examples of Fourier transforms in action are given: removing noise from an electrocardiogram signal, using laser diffraction to calculate the groove spacing on CDs and DVDs, and determining the structure of DNA via x-ray ...
Instructor: Dennis Freeman Description: Sampling produces a discrete-time (digital) signal from a continuous-time (physical) phenomenon. Anti-aliasing and reconstruction filters remove unnecessary frequencies while retaining enough information to reconstruct the ...
Instructor: Dennis Freeman Description: Digital audio, images, video, and communication signals use quantization to create discrete representations of continuous phenomena. Efficient transmission and reconstruction uses techniques such as dithering, progressive ...
Instructor: Dennis Freeman Description: Efficient signal transmission and reception requires wavelengths matching the size of the antenna; for speech, this requires frequencies around the GHz range. Broadcast radio developed AM and FM to produce accurate reception of ...
Instructor: Dennis Freeman Description: Continuing the previous discussion of AM in radio, Prof. Freeman analyzes phase and frequency modulated (PM/FM) signals, before presenting research showing improvement in optical microscopy via phase-modulated illumination.
Instructor: Dennis Freeman Description: Today's lecture discusses an application of Fourier series, exploring how the vocal tract filters frequencies generated by the vocal cords. Speech synthesis and recognition technology uses frequency analysis to accurately ...
Instructor: Dennis Freeman Description: The concept of the Fourier series can be applied to aperiodic functions by treating it as a periodic function with period T = infinity. This new transform has some key similarities and differences with the Laplace transform, its ...
Instructor: Dennis Freeman Description: Today's lecture solidifies the connections between continuous- and discrete-time Fourier series and transforms, converting between the time and frequency domains with familiar tools such as convolution, periodic extension, and ...
Instructor: Dennis Freeman Description: Discrete-time systems can be represented in several ways: difference equations, block diagrams, and operators. Each method requires a different analytical approach. Feedback loops in cyclic systems lead to convergent or divergent ...
Instructor: Dennis Freeman Description: To analyze complicated systems of adders, delays, and gains, factor their polynomial expression into simpler components using the poles. These fundamental modes combine to produce the unit response of a system.
Instructor: Dennis Freeman Description: Drawing analogies with previous concepts in discrete-time systems, this lecture discusses the block diagrams, polynomial expressions, poles, convergence regions, and fundamental modes of continuous-time systems.
Instructor: Dennis Freeman Description: After reviewing concepts in discrete-time systems, the Z transform is introduced, connecting the unit sample response h[n] and the system function H(z). The lecture covers the Z transform's definition, properties, examples, and ...
Instructor: Dennis Freeman Description: Having established representations and analytical methods for discrete-time and continuous-time systems, today's lecture uses the example of a leaky tank to show how Euler and trapezoidal approximations can convert a continuous ...
Instructor: Russ Tedrake Description: Prof. Tedrake introduces the power and complexity of modern control systems, which use feedback to stabilize and compensate for delays and other errors. Examples are taken from his research into perching planes and other ...