Classification of Signals and Systems: Introduction

CLASSIFICATION OF SIGNALS AND SYSTEMS

INTRODUCTION:

A signal, as stated before is a function of one or more independent variables. A signal is a quantitative description of a physical phenomenon, event or process. More precisely, a signal is a function, usually of one variable in time. However, in general, signals can be functions of more than one variable, e.g., image signals. Signals are functions of one or more variables.

Systems respond to an input signal by producing an output signal .

Examples of signals include:

1.           A voltage signal: voltage across two points varying as a function of time.

2.           A force pattern: force varying as a function of 2-dimensional space.

3.           A photograph: color and intensity as a function of 2-dimensional space.

4.           A video signal: color and intensity as a function of 2-dimensional space and time.

A continuous-time signal is a quantity of interest that depends on an independent variable, where we usually think of the independent variable as time. Two examples are the voltage at a particular node in an electrical circuit and the room temperature at a particular spot, both as functions of time.

A discrete-time signal is a sequence of values of interest, where the integer index can be thought of as a time index, and the values in the sequence represent some physical quantity of interest.

A signal was defined as a mapping from a set of the independent variable (domain) to the set of the dependent variable (co-domain). A system is also a mapping, but across signals, or across mappings. That is, the domain set and the co-domain set for a system are both sets of signals, and corresponding to each signal in the domain set, there exists a unique signal in the co-domain set.

System description

The system description specifies the transformation of the input signal to the output signal. In certain cases, a system has a closed form description. E.g. the continuous-time system with description y (t) = x(t) + x(t-1); where x(t) is the input signal and y(t) is the output signal.