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:
- 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.)
- 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)?