SIGNAL , what is definition of SIGNAL , mathematical expressions , Signum function , sgn

By   November 14, 2019

In the communication systems, the word Signal is used very often. Therefore, we must clearly understand its exact meaning.
Basically, the Signal may be defined as the function of one or more independent variables which contains some information. The very familiar examples of electrical signals are voltage and current which are functions of time. The signal is a general term and it is not essential that it will always be used for electrical circuits. We have depicted some of the important signals in table 1.3 along with their mathematical expressions.
Important Signals

S. No. Name of signal and mathematical representation Waveform representation
1. DC signal  
2. Unit step signal  
3. Sinusodial signals  
4. Signum function
sgn (t)=1                        for t > 0
= -1                      for t > 0
= [1]                     for t = 0
5. Rectangular pulse
= 0                            Elsewhere
6. Delta function
Area under delta function:
Shifting property :
Replication property :
7. Decaying exponential function  
8. Rising exponential function  
9. sinc function:
sinc (0) = 1 and sinc (x) = 0
at       x =  1,  2 ……………