3
$\begingroup$

I am currently studying interferometry, but I have only just begun studying signal processing. I want to better understand the effect signal processing can have in maximising signal detection from some hardware device.

My conceptualisation of this is that, when it comes to 'sensing' anything, we must start with hardware in the first place. This hardware then, through some physical mechanism, makes measurements. However, the physical reality is that this 'measurement' is not necessarily perfect – that is, the 'thing' that we want to measure is not necessarily the only 'thing' that was measured by the hardware – and this is where the definition of signal vs noise comes into play – that is, noise is defined to be anything that is not the 'thing' that we're interested in.

So, based on this reasoning, it seems clear to me that, if you want to maximise signal detection, then the 'first order' and most impactful thing you can do is change the hardware somehow to better measure the 'thing' you're interested in and less the 'things' that you're not. However, in practice, detecting more signal by making changes to hardware is not necessarily practical (due to technological factors, economic factors, social factors, diminishing returns, etc.), and so we have a 'second order' method for extracting signal, which is to process the measurements after the hardware makes them. This post-hardware-measurement processing is signal processing, whereby we use mathematical methods to isolate the measurements of the 'thing' that we're interested in (signal), amongst the aggregate measurement, which includes measurements of 'things' that we're not interested in (noise).

In interferometry, people are often trying to measure very subtle 'things', where the hardware device is not necessarily 'good' for the situation (but still feasible), and there is a lot of noise. This is often because such hardware devices are expensive and/or technologically difficult. And when it comes to signal processing, I have read a number of research papers in interferometry that claim that they are using their own/unique/customized/whatever signal processing algorithm to extract signal from these measurements.

My questions are as follows:

  1. Given the constraints in modifying hardware to get an improved measurement in the first place, how much can signal processing actually do in helping us detect more signal? For instance, if we were using a 'bad'/'not-so-good' device to measure some subtle phenomenon, how much could signal processing actually do to help us here (that is, how much of an improvement in the detected signal can signal processing actually get us, despite the fact that the hardware is inadequate)? (Although I have not studied signal processing itself, I have studied mathematics and statistics, and I know that there are all kinds of theorems that allow us to put bounds on things – including in information theory – so I wonder what statements we can make in signal processing to such a question as I have posed here; but, to be clear, I am not necessarily looking for a mathematical and/or rigorous response to this question, so feel free to give any answer that you think is useful in answering such a question.)
  2. In the above interferometry case, why do you think people are using 'custom' signal processing algorithms, as opposed to, what I presume are, 'typical' signal processing algorithms? Can such a practice potentially significantly improve signal detection in such cases? Is it recommended to create 'customized' signal processing algorithms when confronted with such difficult situations ('not-so-good' hardware, subtle signal)?
$\endgroup$
1
  • $\begingroup$ I designed DSP algorithms for interferometers in the past. I discovered the Hilbert transform and Hilbert filters while I was trying to create pseudo-quadrature signals for interferometers. $\endgroup$
    – Ben
    Jul 26 at 12:05
5
$\begingroup$

That's a very broad question, but I'll give it a shot.

1 . ... how much could signal processing actually do to help us here ? ...

That's highly dependent on the specific problem. Sometimes a lot, sometimes not all.

One example for "a lot" is the the acoustic echo canceller in your garden variety Smart Speaker (Amazon Echo, Sonos One, Google Home, etc.) The "thing" that you want to measure is the voice of the customer but the hardware is "bad" since the microphone is right next to the loudspeaker, so if the music is blasting it is orders or magnitude louder at the microphone than the customer's voice . A state of the art echo canceller can improve the signal to noise ratio by north of 30 dB and there are some experimental algorithms that do even better.

  1. ... why do you think people are using 'custom' signal processing algorithms? ...

Because the performance of the algorithm is better the more "knowledge" about your specific application you can build into the algorithm. In general a noise reduction algorithm uses three things:

  1. Knowledge about the signal
  2. Knowledge about the noise
  3. Knowledge about what you want to do with the result and what specific features/properties your application is most sensitive to.

If you know nothing or little about any of these, you can't really do much. Let's look at our Smart Speaker again:

  1. You know that the signal you want to pick up is human speech. That has certain spectral and temporal properties you can use.
  2. You know that the noise is primarily the music that you are playing. You know a whole lot about it and that knowledge actual enables most of the 30 dB gain.
  3. The output will go into a speech recognition system or keyword detector. So you talk to the people who develop these algorithms and learn how they work and what specific signal features (spectral, temporal, linguistic, spatial, ...) are most important

The more you customize, the better it gets. If your transducer in your smart speaker gets non-linear you may want to apply a linearization algorithm that's customized to this transducer. If you linearize, what is the dominant non-linearity? Is it Magnetic-Force/Excursion, the suspension, coil inductance vs current ?. If it's the suspension: is it primarily the spider, air in the box or the surround? If it's the surround, is it pull up, buckling, or the material itself?

It's like peeling an onion, there is always one more layer to dive into and they all can look different from one application to the next.

$\endgroup$
4
  • $\begingroup$ Hmm, that's very interesting. So if we knew that the acoustic signal we wanted to measure had a frequency around 500 kHz, then we could apply a kind of filtering algorithm to exclude anything that deviates too much from 500 kHz? $\endgroup$ Jul 23 at 20:59
  • $\begingroup$ @ThePointer 'xactly. But not only that: if you knew your 500 kHz-centered signal had a specific statistic distribution of say its loudness, you could use that statistic to improve the quality of your estimate for whatever you're observing. List goes on: What if you know the loudness of the ambient noise pulsated at an initially unknown, but slow-changing rate? Could use that. And so on. $\endgroup$ Jul 23 at 21:03
  • $\begingroup$ @MarcusMüller Hmm, very interesting. Thanks for the clarification. $\endgroup$ Jul 23 at 21:05
  • $\begingroup$ @ThePointer: yep, that's probably the easiest it can get. Typical example is power supply noise. You can just filter out 60 Hz, 120Hz, 180 Hz, ... and in may cases that does help (unless you are in Europe, where you want to do 50 Hz etc) . But the trick is always in the details, if your signal also has important features at or near 60Hz you have to get more creative. $\endgroup$
    – Hilmar
    Jul 23 at 21:06

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.