CLASSIFICATION OF SIGNALS AND SYSTEMS

   


 

    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.  

Elementary Signals:  

    The elementary signals are used for analysis of systems. Such signals are,  

Step  

Impulse  

Ramp  

Exponential  

System

    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.  

Continuous-time and discrete-time systems  

    Physically, a system is an interconnection of components, devices, etc., such as a  computer or an aircraft or a power plant.  

    Conceptually, a system can be viewed as a black box which takes in an input signal  x(t) (or x[n]) and as a result generates an output signal y(t) (or (y[n]).  

    A system is continuous-time (discrete-time) when its I/O signals are continuous-time  (discrete-time).



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