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Res.6-007 Signals and Systems

Res.6-007 Signals and Systems (MIT OCW). This consists of 26 video lectures given by Prof. Alan V. Oppenheim, providing an introduction to analog and digital signal processing. The course presents and integrates the basic concepts for both continuous-time and discrete-time signals and systems. Signal and system representations are developed for both time and frequency domains. These representations are related through the Fourier transform and its generalizations, which are explored in detail. Filtering and filter design, modulation, and sampling for both analog and digital systems, as well as exposition and demonstration of the basic concepts of feedback systems for both analog and digital systems, are discussed and illustrated. (from ocw.mit.edu)

Lecture 07 - Continuous-Time Fourier Series

Response of continuous-time LTI systems to complex exponentials: the eigenfunction property; Representation of periodic signals as linear combinations of harmonically related complex exponentials; Fourier series for continuous time: the analysis and synthesis equations; Example: symmetric and anti-symmetric periodic square wave; Approximation of periodic signals; Fourier series convergence.


Go to the Course Home or watch other lectures:

Lecture 01 - Introduction
Lecture 02 - Signals and Systems: Part I
Lecture 03 - Signals and Systems: Part II
Lecture 04 - Convolution
Lecture 05 - Properties of Linear, Time-invariant Systems
Lecture 06 - Systems Represented by Differential Equations
Lecture 07 - Continuous-Time Fourier Series
Lecture 08 - Continuous-Time Fourier Transform
Lecture 09 - Fourier Transform Properties
Lecture 10 - Discrete-Time Fourier Series
Lecture 11 - Discrete-Time Fourier Transform
Lecture 12 - Filtering
Lecture 13 - Continuous-Time Modulation
Lecture 14 - Demonstration of Amplitude Modulation
Lecture 15 - Discrete-Time Modulation
Lecture 16 - Sampling
Lecture 17 - Interpolation
Lecture 18 - Discrete-Time Processing of Continuous-Time Signals
Lecture 19 - Discrete-Time Sampling
Lecture 20 - The Laplace Transform
Lecture 21 - Continuous-Time Second-Order Systems
Lecture 22 - The z-Transform
Lecture 23 - Mapping Continuous-Time Filters to Discrete-Time Filters
Lecture 24 - Butterworth Filters
Lecture 25 - Feedback
Lecture 26 - Feedback Example: The Inverted Pendulum