Lecture 4: Convolution - MIT OpenCourseWare

4 ConvolutionIn 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.

puts, then the response can be constructed as the same linear combination of the responses to each of the basic inputs. Signals (or functions) can be decom-posed as a linear combination of basic signals in a wide variety of ways. For example, we might consider a Taylor series expansion that expresses a func-tion in polynomial form.

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