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If we have a signal and we do not know anything about this signal. We do not know which frequencies contain specific information, and which frequencies does not contain information. Which is the approach for studying this signal and map the possible data to potential frequencies?

For example, when the voice signal was studied, at the beginning the scientists did not know, which frequencies contain the information. They did not know, if the signal or the information is contained in the frequencies 10 GHz - 50 GHZ or in the frequencies 10 MHz - 40 MHz!

It's hard then to decide which sampling frequency we are going to use. If we choose the wrong sampling frequency, then the antialising frequency may throw away the most informative frequencies.

Do we start with trials and errors (or brute force) approach? for example, choosing 1MHz sampling frequency then 2 MHz and so on? until we map all the information to its frequency range. Is there a better approach? Not all experiments are easy to conduct! so it is very costly to do this approach. Consider taking an unknown signal from space; a very rare signal that a very costly radar catch it. That radar sample rate is about 500 GHz and oops! we did not get anything useful from that signal. After years we figure out that we did not find a useful information because the information relies on the frequencies that is larger than 250 GHz.

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  • $\begingroup$ I think that this is an interesting question but the way it is phrased makes it too broad. Do we know this is a data signal? Are we trying to figure out if it is non-random, potentially from an intelligent alien civilisation? Was it received from space indeed? Is this a somewhat hypothetical question (i.e. "Worldbuilding" type of question), because "cost" is a very relative term. $\endgroup$ – A_A Jan 24 '17 at 21:46
  • $\begingroup$ @A_A My question is about any new signal that a scientist can observe it. You may inject sensors deeply inside the brain, and get signals that this is the first time you are dealing with. So, you do not know which frequencies contain the information. I gave an example of "intelligent alien civilisation" because it is the most unknown signal (we may have a general figure about the frequencies of Brain Signals). $\endgroup$ – hbak Jan 25 '17 at 1:38
  • $\begingroup$ @A_A The cost will include the following: we can not repeat the experiment, I mean it needs a lot of time and effort. Also, we cannot get the signal whenever we want, like the intelligent alien civilisation signal example. $\endgroup$ – hbak Jan 25 '17 at 1:40
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If we have a signal and we do not know anything about this signal. We do not know which frequencies contain specific information, and which frequencies does not contain information. Which is the approach for studying this signal and map the possible data to potential frequencies?

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My question is about any new signal that a scientist can observe it.

Before an answer that is closer to the point of the question is provided, I think that it would be beneficial to talk a little bit about how do we acquire signals (and why) just to make sure that we share the same understanding.

The starting point for this will be the second phrase "My question is about any new signal that a scientist can observe".

Observation. It does not occur in isolation. The Scientific Method is a tool to guide investigation that, in an abstract way, is still "trial and error".

  1. It starts with prior knowledge, with suspicion, with a hunch, because of an urban legend, because of other experiments. On the basis of this suspicion, a hypothesis is formulated "Well, if you claim to be a clairvoyant then your predictions of what cards I am holding up without you seeing them, should be better than random chance". Notice here that it is very important for the converse to ALSO be true. "If you are not better than random chance then you are not a clairvoyant, (you are a dice...and a very good one...it's not easy)"

  2. On the basis of this, an experiment is formulated. The way the experiment is structured is extremely important because, usually, there are so many factors that might have an effect on the observed phenomenon. What if the subject gradually learns the deck? What if the assistant holding the cards up is giving off subtle messages? And so on.

  3. Following this is data collection. We find clairvoyants, sit them down across a table and ask them to guess what card we are holding up, covered.

  4. Following this is data analysis which is very much adapted to the experiment in general and by extension to the hypothesis.

  5. Following this we might revisit the hypothesis or the experiment with the newly inferred information and go back through the steps from #1. BUT! We might also decide that we have done everything by the book, all of our colleagues have exhausted their brains and skills in thinking about the problem and to the best of our knowledge and ability we dare to make a statement. "Based on the evidence produced by Mr XYZ, the consensus is that they are most likely to be a clairvoyant". I don't know how they do it but we put them to the test and they are. Here is how we did it in all detail so that an independent researcher can REPLICATE the process to confirm or reject our work. In other words we...

  6. Publish everything. So that others can check our work. In this way at a given point in time, "we" (humans) have a pretty good idea about a phenomenon.

Of course, "we" might choose to ignore all of this...for...reasons. But that's another story.

Therefore, we don't just come across some signal AND THEN try to figure out what the signal is about or how did it come to be. Because OBSERVATION comes AFTER hypothesis. Observation is DESIGNED. It has CONSTRAINTS which are very precisely known. Otherwise, we are just guessing.

The particle accelerator of CERN didn't just pop up in its incredibly expensive existence. Before that one, there were tiny little ones that where very clumsy and...elementary...in their operation.

Electroencephalography didn't just spring into existence. Alpha waves are called Alpha because they were discovered first. They occupy the range between 8Hz-13Hz. But Gamma activity goes even higher, up to 100Hz. Take a 100mV off the shelf volt-meter instrument and squeeze its leads. Yes, it will measure the potential across your hands and you will see the needle moving but from that to being able to make a diagnosis on the basis of electrical activity is a HUGE distance both technologically AND conceptually.

So, in conclusion, we don't just go out there hunting for signals.

Right, done, settled, let's go home.

Not so fast.

SOMETIMES signals do drop from the sky...or...pop up from the sea....or run along a river.

So, what do we do then? No one "ordered" this and we can't send it back.

We still apply the scientific method but making the signal the subject. In other words, the signal is now the "Clairvoyant".

Maybe it's a fault with the equipment. Equipment checked, no faults. Can we reproduce it in the lab? No, it takes a planet Is it confirmed by models? No, no model predicts the existence of such a specimen. How about changing the model? Changing the model could produce a solution but also 23 other perfectly valid (and symmetric) solutions.

So what do we do?

We wait and we collect more data and we perform more experiments and build better models and we think more and do it all over from the beginning.

This also covers the approach for mapping "..which frequencies contain information...".

  • Is the signal similar to background RF radiation?
    • Yes
      • Then...it's noise.
        • Maybe, but maybe it was sent using chaos communications so to an extent it could be indistinguishable from noise.
          • OK so what do we do?
            • Acquire another signal at higher sampling frequency
    • No
      • Does its spectrum look like anything we have seen before?
        • Yes
          • Maybe it is our radiation bouncing back from a planet
        • No
          • Is it repeatable?
            • Yes
              • Is there another physical source of this radiation that could explain it?
            • No
              • Aha! WHEN does it show up?

This is just one of thousands of decision trees you might generate for a problem like this and this is why I wrote earlier that the question is incredibly broad. It cannot be answered with a definite answer but only with the methodology of HOW you answer such questions.

I hope this helps.

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  • $\begingroup$ I am curious to know which is the sampling frequency that is being used in a device that is capturing a signal that is searching for intelligent life outside our solar system? Also, how do we make sure that the anti aliasing filter does not remove the most informative frequencies? $\endgroup$ – hbak Jan 25 '17 at 21:34
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    $\begingroup$ @hbak There will always be limits to what we can "read" or discriminate through noise and these limits are set by material science (and to an extent mathematics). I am not sure about the exact sampling frequency because signals can be brought to lower Intermediate Frequencies and get sampled there. You can download raw data from various telescopes. The antialiasing filter is not a problem, we can move the window of observation anywhere (within limits) $\endgroup$ – A_A Jan 25 '17 at 21:53

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