ABSTRACT
This chapter introduces convolution, which is a fundamental operation in the time domain that gives the response of a linear time-invariant (LTI) system to an arbitrary input, based solely on its impulse response, without any knowledge about the system or its constituents. It begins by explaining two operations that are commonly encountered in convolution, namely, shifting a function in time and folding a function around the vertical axis. The chapter introduces the convolution integral and interpretes graphically, which leads to a general procedure for deriving the convolution integral based on the graphical interpretation. It presents some basic properties of the convolution operation, followed by some important special cases of convolution, namely, convolution of staircase functions and convolution with impulse and step functions. The chapter ends with a summary of some general properties of the convolution integral, illustrated with additional examples.
