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Standard filters in electronic circuits are devices that allow a certain range of frequencies to pass through while attenuate other frequencies. I was wondering if something similar could be built that allowed frequencies to pass through if their amplitude was above a certain threshold.

Detail: Say there are four signals of 100, 200, 300 and 400Hz, each with an amplitude 4, 7, 1 and 12.

The "filter" should be a device that, if given a threshold of 5, completely eliminate the signals of 100 and 300Hz while allowing the one with 200 and 400Hz to pass through ideally without any attenuation.

What circuit or device could possibly do this "physically"? By this, I mean I do not want to digitally find the amplitude spectrum and then reproduce the parts of the signal I want.

P.S: I initially thought that this could be a question better suited for the electronics stackexchange, but I am not looking only for circuits or devices. This is, at least for the moment, a hypothetical question and so I do not really have a strict nature of the signals. They could be currents, voltages, optical amplitudes, sound amplitudes or water waves or anything else. This is why I chose to post it here. As for tags, I am not sure what to put here. There appear to be no tags regarding filtering. Going with a generic signal processing one for now.

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Typically we work with linear filters precisely because they do not discriminate based on signal amplitude. This is almost the definition of a linear filter.

This means that what you are asking for requires non-linear signal processing elements. The simplest example of a filter with an amplitude dependent output is an amplifier which saturates. Say we have an amplifier that increases a signal by (100x) as long as the input is less than $1V$. However, if the signal is $1V$ or larger the output is simply $100 V$.

Now imagine we have two tones, one at 100 Hz with an amplitude of 100 mV and one at 200 Hz with an amplitude of 10 V. Initially the 200 Hz tone is (100x) (or 40 dB) larger than the 100 Hz tone. If we pass the two tones through the amplifier then the 100 Hz tone will now be 10 V and the 200 Hz tone will now be 100 V. Now the 200 Hz tone is only (10x) (or 20 dB) larger than the 100 Hz signal. We could then divide the entire signal by a factor of (100x) so that the 100 Hz tone would again be at 100 mV but the 200 Hz would not be at 1 V rather than 10 V. The net effect of the saturating amplifier followed by a divider circuit is a circuit which applied 20 dB of suppression to the high amplitude signal.

This doesn't do exactly what you asked for but it is a step in the right direction and I hope the insight about the requirement for a non-linear circuit will be helpful for you.

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If you want to talk about waves on water, that would be a dam, but the wave that emerges on the far side would most likely be distorted. I believe a pair of diodes would do something similar for a low voltage AC signal.

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  • $\begingroup$ Could you offer some more information or a link to a resource too? Thanks! $\endgroup$
    – Paddy
    Commented Nov 13, 2020 at 16:08
  • $\begingroup$ As I recall, there is a threshold voltage for a diode to conduct in the forward direction. $\endgroup$
    – R.W. Bird
    Commented Nov 16, 2020 at 13:32
  • $\begingroup$ True. But I do not think that is not helpful. I believe the diode does not look at signals in terms of their frequency. A "triangle" wave would pass completely if its amplitude was sufficiently high even if certain components of the wave did not have the requisite amplitude. $\endgroup$
    – Paddy
    Commented Nov 16, 2020 at 17:57

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