Introduction to Algorithms - Lecture 21: Dynamic ...
Introduction to Algorithms - Lecture 21: Dynamic Programming III: ...
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
Introduction to Algorithms - Lecture 10: Open Addressing, ...
Introduction to Algorithms - Lecture 10: Open Addressing, Cryptographic ...
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
Introduction to Algorithms - Lecture 14: Depth-First Search ...
Introduction to Algorithms - Lecture 14: Depth-First Search (DFS), ...
Description: This lecture covers depth-first search, including edge classification, and how DFS is used for cycle detection and topological sort. Instructor: Erik Demaine
Introduction to Algorithms - Lecture 15: Single-Source ...
Introduction to Algorithms - Lecture 15: Single-Source Shortest Paths ...
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
Introduction to Algorithms - Lecture 19: Dynamic ...
Introduction to Algorithms - Lecture 19: Dynamic Programming I: Fibonacci, ...
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. ...
Introduction to Algorithms - Recitation 10: Quiz 1 Review
Introduction to Algorithms - Recitation 10: Quiz 1 Review
Description: This recitation covers several practice problems for Quiz 1, taken from previous semesters of 6.006. Instructor: Victor Costan
Signals and Systems - Lecture 20: Applications of Fourier ...
Signals and Systems - Lecture 20: Applications of Fourier Transforms
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 ...
Signals and Systems - Lecture 21: Sampling
Signals and Systems - Lecture 21: Sampling
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 ...
Signals and Systems - Lecture 22: Sampling and Quantization
Signals and Systems - Lecture 22: Sampling and Quantization
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 ...
Signals and Systems - Lecture 23: Modulation, Part 1
Signals and Systems - Lecture 23: Modulation, Part 1
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 ...
Signals and Systems - Lecture 24: Modulation, Part 2
Signals and Systems - Lecture 24: Modulation, Part 2
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.
Signals and Systems - Lecture 15: Fourier Series
Signals and Systems - Lecture 15: Fourier Series
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 ...
Signals and Systems - Lecture 16: Fourier Transform
Signals and Systems - Lecture 16: Fourier Transform
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 ...
Signals and Systems - Lecture 19: Relations Among Fourier ...
Signals and Systems - Lecture 19: Relations Among Fourier Representations
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 ...
Signals and Systems - Lecture 2: Discrete-Time (DT) Systems
Signals and Systems - Lecture 2: Discrete-Time (DT) Systems
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 ...
Signals and Systems - Lecture 3: Feedback, Poles, and ...
Signals and Systems - Lecture 3: Feedback, Poles, and Fundamental Modes
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.
Signals and Systems - Lecture 4: Continuous-Time (CT) ...
Signals and Systems - Lecture 4: Continuous-Time (CT) Systems
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.
Signals and Systems - Lecture 5: Z Transform
Signals and Systems - Lecture 5: Z Transform
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 ...
Signals and Systems - Lecture 7: Discrete Approximation of ...
Signals and Systems - Lecture 7: Discrete Approximation of Continuous-Time ...
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 ...
Signals and Systems - Lecture 10: Feedback and Control
Signals and Systems - Lecture 10: Feedback and Control
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 ...