Lecture 4: Convolution - MIT OpenCourseWare

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4ConvolutionIn Lecture 3 we introduced and defined a variety of system properties towhich we will make frequent reference throughout the course. Of particularimportance are the properties of linearity and time invariance, both becausesystems with these properties represent a very broad and useful class and be-cause with just these two properties it is possible to develop some extremelypowerful tools for system analysis and linear system has the property that the response to a linear combina-tion of inputs is the same linear combination of the individual responses. Theproperty of time invariance states that, in effect, the system is not sensitive tothe time origin.

time and discrete-time signals as a linear combination of delayed impulses and the consequences for representing linear, time-invariant systems. The re-sulting representation is referred to as convolution. Later in this series of lec-tures we develop in detail the decomposition of signals as linear combina-

  Time, Discrete, Signal, Mit opencourseware, Opencourseware, Convolutions, Discrete time signals