Signal to noise ratio for a non-physical property

datamathnoisesignalsignal-to-noise

The signal to noise ratio for a voltage, current, or power is easy to understand, but how do I calculate the SNR when the signal is not a physical property, but instead an abstract quantity?

I'll try and be clearer: I'm doing a theoretical project, and I have created a computer program that measures the solid angles that a simulated point subtends a number of simulated detectors. It then calculates the position of the point using these solid angles. I want to simulate what would happen if the detectors measure the solid angles with a slight inaccuracy. To do this I have added random numbers (between 0 and 0.01) to all of the simulated detector readings. I have called this noise, but I'm not sure if that is the correct term.

The detector readings can normally give a reading between 0 and 2pi, where 0 is when the point lies on the plane of the detector, but outside its perimeter, and 2pi is when the point lies on the plane of the detector, and in the center of detector perimeter. (They are 3D angles). This can be seen in this picture.

I want to express this noise as a signal to noise ratio. Can I just do:

$$0.01/2pi = 0.00159\%$$

Where 0.01 is the maximum size of deviation from the true value, and 2pi is the maximum size of the true value.


Here's another way to ask this question.

In my program the noise is simulated as:

$$Y=net(X+N)$$

Where \$Y\$ is the Position, \$net\$ is the function that maps \$X\$ onto \$Y\$, and \$N\$ is the noise.

I want to modify this function so instead of including \$N\$, it instead includes the Signal-To-Noise ratio. This is so I can do a sweep of the SNR to see how much noise my function \$net\$ can tolerate. How can I do this?

Best Answer

When talking about abstract quantities, we generally stop talking about "noise" and instead start talking about probability distribution functions (PDFs) and confidence levels.

You might be able to say, for example, that the answer (position) is correct to within 0.1 meters 95% of the time. You need to establish what your correctness criteria are for your application, and analyze how the PDF of the raw data gets transformed into the PDF of the result.

For a more detailed description, do some research into how the results are described for GPS receivers.

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