page_title: Poisson wavelet
section_title: A class of complex wavelets associated with the Poisson kernel
hierarchical_section_title: Poisson wavelet / A class of complex wavelets associated with the Poisson kernel
caption_attribution_description: English: The image is that of the imaginary parts of the Poisson wavelet &#x03C8; n ( t ) {\displaystyle \psi _{n}(t)} for n = 1 , 2 , 3 , 4 {\displaystyle n=1,2,3,4} .
context_page_description: In mathematics, in functional analysis, several different wavelets are known by the name Poisson wavelet. In one context, the term "Poisson wavelet" is used to denote a family of wavelets labeled by the set of positive integers, the members of which are associated with the Poisson probability distribution. These wavelets were first defined and studied by Karlene A. Kosanovich, Allan R. Moser and Michael J. Piovoso in 1995–96. In another context, the term refers to a certain wavelet which involves a form of the Poisson integral kernel. In a still another context, the terminology is used to describe a family of complex wavelets indexed by positive integers which are connected with the derivatives of the Poisson integral kernel.
caption: The graphs of the imaginary parts of the Poisson wavelet 
    
      
        
          
            ψ
            
              n
            
          
          (
          t
          )
        
      
      {\displaystyle \psi _{n}(t)}
    
   for 
    
      
        
          n
          =
          1
          ,
          2
          ,
          3
          ,
          4
        
      
      {\displaystyle n=1,2,3,4}
    
  .
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