Patent ID: 11927501
Assignee: SAFRAN
Field: Measurement (Instruments)
Classification: CPC G | IPC F  G

Claim 3:
4. The monitoring method according to claim 3, wherein the determination of the selective spectral kurtosis of the digital signal comprises the following sub-steps:
determining (E101) a short-term Fourier transform of the digital signal defined by

X(iΔt;mΔf)DFTnδt→mΔfNh{h(nδt−iΔt)x(nδt)} 0≤m<S 

with Δt/δt=Nh(1−ρ) where ρ refers to the rate of overlap of the sliding window and S=T/Δt is the digital length of the short-term Fourier transform with respect to the variable iΔt and T is the duration of acquisition of the signal;
normalizing (E102), for each frequency mΔf, the short-term Fourier transform obtained as follows:, X
     N
    
    (
    
     
      i
      ⁢
      Δ
      ⁢
      t
     
     ;
     
      m
      ⁢
      Δ
      ⁢
      f
     
    
    )
   
   =
   
    
     X
     ⁡
     (
     
      
       i
       ⁢
       Δ
       ⁢
       t
      
      ;
      
       m
       ⁢
       Δ
       ⁢
       f
      
     
     )
    
    
     
      σ
      x
     
     (
     
      m
      ⁢
      Δ
      ⁢
      f
     
     )
    
   
  
  ,, where
   ⁢
      
   
    
     σ
     x
    
    (
    
     m
     ⁢
     Δ
     ⁢
     f
    
    )
   
  
  =
  
   
    
     1
     S
    
    ⁢
    
     
      ∑
       
     
     
      n
      =
      0
     
     
      S
      -
      1
     
    
    ⁢
    
     
      
       ❘
       "\[LeftBracketingBar]"
      
      
       X
       ⁡
       (
       
        
         i
         ⁢
         Δ
         ⁢
         t
        
        ,
        
         m
         ⁢
         Δ
         ⁢
         f
        
       
       )
      
      
       ❘
       "\[RightBracketingBar]"
      
     
     2
    
   
  
 

 is the standard deviation of the short-term Fourier transform with respect to the time variable at the frequency mΔf;
determining (E103), for each frequency mΔf, the discrete Fourier transform with respect to a time axis, Γ
     
      2
      ⁢
      X
     
    
    (
    
     
      
       a
       ·
       Δ
      
      ⁢
      α
     
     ;
     
      m
      ⁢
      Δ
      ⁢
      f
     
    
    )
   
   =
   
    
     1
     S
    
    ⁢
    
     DFT
     
      
       i
       ⁢
       Δ
       ⁢
       t
      
      →
      
       a
       ⁢
       Δ
       ⁢
       α
      
     
     S
    
    ⁢
    
     {
     
      
       
        ❘
        "\[LeftBracketingBar]"
       
       
        
         X
         N
        
        (
        
         
          i
          ⁢
          Δ
          ⁢
          t
         
         ;
         
          m
          ⁢
          Δ
          ⁢
          f
         
        
        )
       
       
        ❘
        "\[RightBracketingBar]"
       
      
      2
     
     }
    
   
  
  ,
 

where, Δα
  =
  
   1
   
    Δ
    ⁢
    
     t
     ·
     S
    
   
  
 

 is the frequency resolution with respect to the secondary frequency aΔα;
determining (E104) the selective spectral kurtosis by means of the following functional:, KSS
    
     4
     ⁢
     X
    
    
     f
     ⁢
     1
    
   
   (
   
    m
    ⁢
    Δ
    ⁢
    f
   
   )
  
  =
  
   
    ∑
    
     a
     =
     
      c
      ·
      k
     
    
   
   
    
     
      
       ❘
       "\[LeftBracketingBar]"
      
      
       
        Γ
        
         2
         ⁢
         X
        
       
       (
       
        
         a
         ⁢
         Δα
        
        ;
        
         m
         ⁢
         Δ
         ⁢
         f
        
       
       )
      
      
       ❘
       "\[RightBracketingBar]"
      
     
     2
    
    .
   
  
 

with c=1, 2, 3 . . . and such that c<S/2k−1.