Sinusoidal Signals
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Note: This course is being offered this summer by Stanford as an online course for credit. It can be taken individually, or as part of a master’s degree or graduate certificate earned online through the Stanford Center for Professional Development. The goals for the course are to gain a facility with using the Fourier transform, both specific techniques and general principles, and learning to recognize when, why, and how it is used....more
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Introduction to applied linear algebra and linear dynamical systems, with applications to circuits, signal processing, communications, and control systems. Topics include: Least-squares aproximations of over-determined equations and least-norm solutions of underdetermined equations. Symmetric matrices, matrix norm and singular value decomposition. Eigenvalues, left and right eigenvectors, and dynamical interpretation. Matrix...more
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Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODEs) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's,...more
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Guest Lecturer, Setup of the Ice Cream Store Problem, with Customer, Cashier, Clerk, and Manager Threads, The Different Constraints on the Various Types of Threads, Writing the Main Function, Spawning the Various Threads, Handling the Manager-Clerk Interaction Using the Inspection Struct, Which Uses a Semaphore to Signal to the Manager That the Clerk Is Ready for Inspection, As Well as a Semaphore that Ensures that the Clerk Will Wait for...more
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We look at two settings with asymmetric information; one side of a game knows something that the other side does not. We should always interpret attempts to communicate or signal such information taking into account the incentives of the person doing the signaling. In the first setting, information is verifiable. Here, the failure explicitly to reveal information can be informative, and hence verifiable information tends to come out even...more
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Effect On Fourier Transform Of Shifting A Signal, Resulting Delay Formula (Shift Theorem), Effect Of Scaling The Time Signal, Stretch Theorem Formula/ Interpretation, Convolution In Context Of Fourier Transforms; Multiplying Two Signals In Frequency, Resulting Convolution Formula
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Review Of Main Properties Of The Shah Function, Setup For The Interpolation Problem, Bandwidth Assumption, Solving For Exact Interpolation For Bandlimited Signals, Periodizing The Signal By Convolution With The Shah Function, Solution Of The Interpolation Problem
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Sexual selection is a component of natural selection in which mating success is traded for survival. Natural selection is not necessarily survival of the fittest, but reproduction of the fittest. Sexual dimorphism is a product of sexual selection. In intersexual selection, a sex chooses a mate. In intrasexual selection, individuals of one sex compete among themselves for access to mates. Often honest, costly signals are used to help the...more
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Summary Of Previous Lecture (Analyzing General Periodic Phenomena As A Sum Of Simple Periodic Phenomena), Fourier Coefficients; Discussion Of How General The Fourier Series Can Be (Examples Of Discontinuous Signals), Discontinuity And Its Impact On The Generality Of The Fourier Series, Infinite Sums To Represent More General Periodic Signals, Summary Of Convergence Issues, Convergence: Continuous Case, Smooth Case (Fourier Series...more
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Periodicity; How Sine And Cosine Can Be Used To Model More Complex Functions, Example Of Periodizing A Signal, Discussion Of How To Model Signals With Sinusoids, "One Period, Many Frequencies" Idea In Modeling Signals, Modeling A Signal As The Sum Of Modified Sinusoids (Formula), Complex Exponential Notation, Symmetry Property Of The Complex Coefficients In The Fourier Series, Discussion Of The Generality Of The Fourier Series...more
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Correction To The End Of The CLT Proof, Discussion Of The Convergence Of Integrals; Approaches To Making A More Robust Definition Of The Fourier Transform, Examples Of Problematic Signals, How To Approach Solving The Problem; Choosing Basic Phenomena To Use To Explain Others, Identifying The Best Class Of Signals For Fourier Transforms; + Their Properties, The Definition Of The Class Of Rapidly Decreasing Functions, Rationale For Why...more
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Review Of Basic DFT Definitions, Special Case: Value Of The DFT At 0, Two Special Signals: One Vector, Delta Vector, DFT Of Deltas, Complex Exponentials, DFT As Nxn Matrix Multiplication, Periodicity Of Input/Output Signals In The DFT, Result Of Periodicity: Indexing, Result Of Periodicity: Duality
