Transforms - Substitution(Frequency Shifting)

 
   
     
       

Laplace Transform

       

Substitution / Frequency Shifting

       

          This property describes how multiplying a function by an exponential \( e^{at} \) shifts its Laplace transform along the frequency axis.        

        Frequency shifting in Laplace domain.      
     
       
         

Formula:

         
           

\[ \mathcal{L}\{e^{at}f(t)\} = F(s - a) \]

         
         

Applications:

         
               
  • Control system design (pole shifting).
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  • Used in signal modulation.
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  • Stability and response shaping in filters.
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