Energy transfer filters

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The comparison between energy transfer filter and conventional signal filters.

Energy transfer filters are one type of nonlinear filter that operates on the principle of moving or transferring the signal energy of one frequency to another frequency by applying the properties of nonlinear dynamics.

Design

The concept of energy transfer filters is shown as below:

Given one (several) specific inputs, the frequency components of which are over a frequency band (a,b) and a corresponding desired output spectrum (spectra) over a frequency band (c,d) which is different from (a,b), design a nonlinear filter of the form$y(k)-\sum _{l_1=1}^{K_y}{c}_{10}(l_1)y(k-l_1)=\sum _{n=N_0}^N\sum _{l_1=1}^{K_{nu}}...\sum _{l_n=l_{n-1}}^{K_{nu}}{\overline{c}}_{0n}(l_1,...,l_n)\prod _{i=1}^{n}u(k-l_i)$ to implement the signal energy transfer from the input frequency band (a,b) to the output frequency band (c,d)

The design involves the following steps:

1. Determine the filter structure.
2. Map the time domain model description into the frequency domain.
3. Express the output spectrum in terms of the input spectrum and the filter time domain model parameters.
4. Conduct the design based on the expression obtained in step 3.
5. Realise the design.

Energy Focus Filters

Example of an energy focus filter that centralizes the energies of wave at frequency bands [a,b] and [e,f] to freqeuncy band [c,d]

Energy focus filters are one type of enrgy transfer filter that exploit the energy transfer phenomena to centralize signal ergies to a specified frequency band.

Benefits and possible applications

The advantage of energy transfer filters, which can move energy to another frequency band, or spreading it over a wide frequency range, can help to reduce the vibrations or noises transmitted to output by migrating the noise inputs from resonant frequencies. On the other hand, it can also be used to assist people with impaired hearing by migrating whose frequency region with damaged hearing ability input to that with non-affected frequency region.

Reference

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