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Is there anyone having the experience of taking the wavelet funtion as a transfer function?

That is: if we have $\psi_{m,n}(x)=a^{-m/2}\psi(a^{-m}x-nb)$, $\psi_{m,n}$ is the dilated and shifted version of a mother wavelet function $\psi(x)$, $m$ and $n$ are the scale and time variables respectively. Then we take $\psi_{m,n}$ as a transfer function and its input is function $f(x)$, and output is $g(x)$: $g(x) = \psi_{m,n}(f(x))$.

My question is:

  1. for particular input $f(x)$, if there is some relationship between $g(x)$ and $\psi_{m,n}$?

  2. Is there any research field which are focusing on the properties and applications of the transfer function?

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  • $\begingroup$ I do not understand your notation: $g(x) = \psi_{m,n}(f(x))$. Could you please explain it? $\endgroup$ – Laurent Duval Mar 10 at 15:51
  • $\begingroup$ Hi, $g(x)$ can be seen as the composition function, whose input is $x$. Then $f(x)$ is the intermediate output and the $\psi_{m,n}(f(x))$ is the final output. So we have function maps: $x->f(x)->\psi_{m,n}(f(x))$. If map $f(x)$ is fixed, I would like to find something interesting on how $f(x)$ and $\psi_{m,n}$ affects $g(x)$ frome other pespectives such as frequency domain or information entropy view. $\endgroup$ – hcao Mar 11 at 1:52
  • $\begingroup$ So a form of warping of the variable $x$? $\endgroup$ – Laurent Duval Mar 12 at 5:00

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