Average waveform or calculated values?

[JaWiB]

I have an experiment where I calculate a value based on a waveform acquired by a digitizing oscilloscope. Since the signal is very noisy, I need to average the results many times to get a reasonably accurate value for each measured data point. My question is how should I spend the time averaging (or whether it even matters). On the one hand, I can take many waveforms and then average them together (the digitizer has a function to do this). On the other hand, I could take one waveform and perform my calculation (roughly speaking, just a numerical integration over time) and average many results of the calculation.

It seems to me that both methods should be mathematically equivalent as basically a sum over integrals or an integral over sums, but I can't help but feel like I'm missing something.

 

[Number Nine]

Do you know anything about the noise? High frequency noise can be attenuated by a variety of smoothing techniques.

How you approach this will depend on what kind of analysis you're doing, and what you know about the noise.

 

[JaWiB]

Well, the primary issue is high frequency noise and it's probably due to a large number of things. The signal comes from a lock-in amplifier which already has a low-pass filter.

Perhaps it helps if I describe the calculation. The first half of the signal represents a measurement taken under one experimental condition while the second is taken under another condition. We integrate over part of the first half, and (ideally) the same part of the second half, and the final data point is the difference between those integrals. I can either do those integrals on a single waveform, or let the digitizer average a bunch of times and then do the integral. As far as I know, the other students in the lab have always done the latter--I just don't know if it matters.

 

[ImaLooser]

Well, the primary issue is high frequency noise and it's probably due to a large number of things. The signal comes from a lock-in amplifier which already has a low-pass filter.

Perhaps it helps if I describe the calculation. The first half of the signal represents a measurement taken under one experimental condition while the second is taken under another condition. We integrate over part of the first half, and (ideally) the same part of the second half, and the final data point is the difference between those integrals. I can either do those integrals on a single waveform, or let the digitizer average a bunch of times and then do the integral. As far as I know, the other students in the lab have always done the latter--I just don't know if it matters.

Integration is a linear operator, so the sum of integrals is always the same as the integral of sums.

 

[blue_raver22]

As a scientist, it is important to consider the purpose and goals of your experiment when deciding between using an average waveform or calculated values. Both methods have their advantages and disadvantages, and it ultimately depends on what you are trying to achieve with your experiment.

If your goal is to obtain a more accurate and precise value for each data point, then averaging the waveforms may be a more suitable approach. This is because averaging multiple waveforms can help reduce the impact of noise and variability in the data, resulting in a more reliable and consistent value.

However, if your experiment is more focused on understanding the overall trend or pattern of the data, then using calculated values may be a better option. This approach allows you to analyze the data in a more simplified form, without being influenced by the noise and fluctuations in individual waveforms.

In terms of the time spent averaging, it is important to strike a balance between obtaining enough data points for a statistically significant result, while also considering the practical limitations of time and resources. It may be helpful to conduct a pilot study to determine the optimal number of waveforms or calculated values to use for your experiment.

In conclusion, both methods have their merits and it ultimately depends on the specific goals of your experiment. As a scientist, it is important to carefully consider these factors and choose the approach that will best answer your research question.