# Linear Systems

• Ram P. Kanwal

## 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
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