# Take a wavelet function as a transfer funtion

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?

• I do not understand your notation: $g(x) = \psi_{m,n}(f(x))$. Could you please explain it? – Laurent Duval Mar 10 at 15:51
• 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. – hcao Mar 11 at 1:52
• So a form of warping of the variable $x$? – Laurent Duval Mar 12 at 5:00