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I have read in many papers that time complexity of WPT is $O(N \log(N))$, but I would like to know what is the effect of Levels in the time complexity.

Must it be one of the following ?

  • $O(2^{L} ~N~ \log(N))$
  • $O(2^{L+1} ~N~ \log(N))$
  • $O(L ~N ~\log(N))$

$ L$ is the number of decomposition levels

Can anyone helps which is true?

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I just found the answer in a paper. so thought it might be useful for someone.
If we decompose a signal with length of $N$ to $L$ level then time complexity is
$O(L\times Nlog_{2}N)$

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