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I have calculated the inverse transfer function of a low pass filter, and was wanting to design a circuit so that the original filters effect will be cancelled by its inverse. What would be the most effecient way to achieve this?

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  • \$\begingroup\$ It depends on the TF. Please add it. Also, in practice this cancellation will have major limitations. \$\endgroup\$ Oct 5, 2015 at 2:59
  • \$\begingroup\$ Lowpass order? First or second order? \$\endgroup\$
    – LvW
    Oct 5, 2015 at 7:53
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    \$\begingroup\$ @Rob please don't deface your questions, even if you're not interested in it any more someone else may be interested in the answers. \$\endgroup\$
    – PeterJ
    Oct 5, 2015 at 9:56

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Filtering inverse to a first-order lowpass is very simple:

Lowpass: H1(s)=1/(1+sRC)

Inverse: H2=1+sRC

The inverse filter can be realized with an opamp and R-C-feedback (R between output and inv. input, C between inv. input and ground). The non-inv. opamp input terminal is used for signal input.

In case o f a second-order lowpass a third quadratic term (s²T²) must be added (second-order differentiator).

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The most efficient way to do this is to use a simulator such as LTSpice. You model your low pass filter and then follow that with an appropriate filter to level out the frequency response. Be prepared to compromise though because, a low pass filter will eventually produce an output (beyond the 3dB point) that is down in the noise and no amount of trying to recover your signal will result in anything meaningful.

I had to do this on one job where we didn't have enough room to put a decent anti-alias filter in front of an ADC so, we went heavy-handed with a sloppy RC LPF and attempted recovery after the signal had been re-constituted to analogue. It worked OK and we recovered our signal at the right amplitude.

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