Extension of the additive model

Model:

• Proposed partial model is non stationary with linear amplitude and linear frequency changes for each signal block $r$

  
  

  $$p_r(n) = (A_r+a_rn) \cos( (\Omega_r +\omega_r n)n +\phi_r)$$
  
  

• Due to continuity constraints the partials of consecutive blocks are not independent $\Rightarrow$ tracking!

Parameter estimation

• Due to complicated distortion of partial spectra Fourier analysis is difficult to apply.

• Adaptive solution: Minimize squared error between model $x(n)$ and signal $s(n)$ by gradient descent
  
  $$E = \sum_n(s(n)-x(n))^2 = \hbox{Min}$$