## Abstract

Recall that we define a function as a rule that maps (transforms) numbers into numbers, whereas a functional maps functions into numbers. An *operator* maps functions into functions. Let a class of functions be given, all defined for a variable, say, time *t*, -∞ <*t* < ∞. Then an operator (transformation) *L* assigns a member of this class (inputs, excitations, or signals) to members of a second class of functions (outputs or responses). We shall use the symbol *x*(*t*) for an input and *y*(*t*) for the corresponding output. A system is a mathematical model of a physical device and is represented by an operator *L*. Then *y*(*t*) is called the response of *x*(*t*) due to the given system. A system is often represented by a box as shown in Figure 14.1.

## Keywords

Linear System Impulse Response Step Response Impulse Response Function Sampling Theorem## Preview

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