Energy (signal processing)

In <a href="/facts/Signal_processing/Npaja6zb">signal processing</a>, the energy 
 
 
 
 
 E
 
 s
 
 
 
 
 {\displaystyle E_{s}}
 
 of a continuous-time signal x(t) is defined as the area under the squared magnitude of the considered signal i.e., mathematically

E
 
 s
 
 
  
  
 =
  
  
 ⟨
 x
 (
 t
 )
 ,
 x
 (
 t
 )
 ⟩
  
  
 =
 
 ∫
 
 −
 ∞
 
 
 ∞
 
 
 
 
 |
 
 x
 (
 t
 )
 
 
 |
 
 
 2
 
 
 
 d
 t
 
 
 {\displaystyle E_{s}\ \ =\ \ \langle x(t),x(t)\rangle \ \ =\int _{-\infty }^{\infty }{|x(t)|^{2}}dt}
 
<a class="footnote-ref" id="fnref:1" href="#fn:1">1</a>
Unit of 
 
 
 
 
 E
 
 s
 
 
 
 
 {\displaystyle E_{s}}
 
will be (unit of signal)2.

And the energy 
 
 
 
 
 E
 
 s
 
 
 
 
 {\displaystyle E_{s}}
 
 of a discrete-time signal x(n) is defined mathematically as

E
          
            s
          
        
         
         
        =
         
         
        ⟨
        x
        (
        n
        )
        ,
        x
        (
        n
        )
        ⟩
         
         
        =
        
          ∑
          
            n
            =
            −
            ∞
          
          
            ∞
          
        
        
          
            |
          
          x
          (
          n
          )
          
            
              |
            
            
              2
            
          
        
      
    
    {\displaystyle E_{s}\ \ =\ \ \langle x(n),x(n)\rangle \ \ =\sum _{n=-\infty }^{\infty }{|x(n)|^{2}}}

Energy (signal processing) open-in-new

Energy (signal processing)